Finite Group Databasebeta

← #20249778

Subgroups — #20249778

Order 6016.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094019C211yesmaximal, characteristic, complemented
2C2×#13093992C211yesmaximal, characteristic
3#15689060C211yesmaximal, characteristic, complemented
4#15689046C211yesmaximal, characteristic, complemented
5#15689039C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic, complemented
7#15689038C211yesmaximal, characteristic, complemented
8#15689026C211yesmaximal, characteristic, complemented
9#15689023C211yesmaximal, characteristic, complemented
10#15689016C211yesmaximal, characteristic, complemented
11#15689013C211yesmaximal, characteristic, complemented
12#15689012C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14#15688978C211yesmaximal, characteristic, complemented
15C47×#394C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19#13094019—24no—
20#13093992—24no—
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×C4⋊Dic47C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic, complemented
30C2×C22⋊Dic47C2211yescharacteristic, complemented
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic, complemented
42C2×C4×Dic47C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C22×D4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic, complemented
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic, complemented
51C2×C22⋊C4×C47C2211yescharacteristic, complemented
52#95×C47C2211yescharacteristic, complemented
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C23×D47—22no—
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—41no—
59C23×D47—41no—
60C23×D47—41no—
61C23×D47—41no—
62C23×D47C2311yescharacteristic
63C23×D47C2311yescharacteristic
64C2×D4×C47—22no—
65C2×D4×C47—22no—
66C2×D4×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—41no—
76C2×C22⋊D47—41no—
77C2×C22⋊D47—41no—
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22×Dic47C2311yescharacteristic
84C4⋊C4×C47—22no—
85C22⋊C4×C47—22no—
86C22⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C22⋊Dic47—22no—
90C22⋊Dic47—41no—
91C22⋊Dic47—41no—
92C22⋊Dic47—41no—
93C22⋊Dic47—41no—
94(C2×D47)⋊C4—22no—
95(C2×D47)⋊C4—22no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—41no—
99(C2×D47)⋊C4—41no—
100(C2×D47)⋊C4—41no—
101(C2×D47)⋊C4—41no—
102(C2×D47)⋊C4—41no—
103(C2×D47)⋊C4D414yes—
104C4⋊Dic47—22no—
105C4⋊Dic47—41no—
106C4⋊Dic47—41no—
107Dic47⋊C4—22no—
108Dic47⋊C4—41no—
109C4×Dic47—22no—
110C4×Dic47—41no—
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×C47—21no—
123C23×C47—21no—
124C23×C47#4112yes—
125C23×C47C2411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47—44no—
139C22×D47—44no—
140C22×D47—44no—
141C22×D47—44no—
142C22×D47—44no—
143C22×D47—44no—
144C22×D47—44no—
145C22×D47C2×D412yes—
146C22×D47#4112yes—
147D4×C47—44no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
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×C47C2×D412yes—
163C22⋊D47—44no—
164C22⋊D47—44no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
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×Dic47C2×D412yes—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—22no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47C22×D411yescharacteristic
198C22×C47C2×#4111yescharacteristic
199C22×C47C2×#4111yescharacteristic
200C22×C47H(5,𝔽2)11yescharacteristic
201C22×C47H(5,𝔽2)11yescharacteristic
202C22×C47H(5,𝔽2)11yescharacteristic
203C22×C47H(5,𝔽2)11yescharacteristic
204C2×D47—22no—
205C2×D47—22no—
206C2×D47—22no—
207C2×D47—22no—
208C2×D47—22no—
209C2×D47—22no—
210C2×D47—416no—
211C2×D47—41no—
212C2×D47—41no—
213C2×D47—41no—
214C2×D47—41no—
215C2×D47—41no—
216C2×D47—41no—
217C2×D47—41no—
218C2×D47—41no—
219C4×C47—22no—
220C4×C47—41no—
221C4×C47—41no—
222C4×C47—41no—
223C4×C47—41no—
224Dic47—22no—
225Dic47—41no—
226Dic47—41no—
227Dic47—41no—
228Dic47—41no—
229Dic47—41no—
230#2685—471nomaximal, Sylow
231C2×C47—42no—
232C2×C47—81no—
233C2×C47#53511yescharacteristic
234C2×C47#53811yescharacteristic
235C2×C47#53811yescharacteristic
236C2×C47#54611yescharacteristic
237C2×C47#54611yescharacteristic
238C2×C47#55111yescharacteristic
239C2×C47#56011yescharacteristic
240D47—42no—
241D47—42no—
242C2×#126—471no—
243C2×#120—471no—
244#399—471no—
245#396—471no—
246#394—471no—
247#394—471no—
248#394—471no—
249#394D4711yescharacteristic, complemented
250#390—471no—
251#390—471no—
252#388—471no—
253#388—471no—
254#388—471no—
255#379—471no—
256#379—471no—
257C47#268511yescharacteristic, complemented, Sylow
258C25—471no—
259C22×D4—471no—
260C22×D4—471no—
261C22×D4C2×D4711yescharacteristic
262#126—944no—
263#120—944no—
264C2×C4⋊C4—471no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4—471no—
267C2×C4⋊C4—471no—
268C2×C4⋊C4—471no—
269C2×C4⋊C4C2×D4711yescharacteristic, complemented
270C2×C22⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—471no—
273C2×C22⋊C4—471no—
274C2×C22⋊C4—471no—
275C2×C22⋊C4—471no—
276C2×C22⋊C4—471no—
277C2×C22⋊C4—471no—
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—471no—
282C2×C22⋊C4—471no—
283C2×C22⋊C4—471no—
284C2×C22⋊C4—471no—
285C2×C22⋊C4C2×D4711yescharacteristic
286C2×C22⋊C4C2×D4711yescharacteristic
287C2×C22⋊C4C2×D4711yescharacteristic, complemented
288C2×C22⋊C4C2×D4711yescharacteristic, complemented
289C2×C42—471no—
290C2×C42—471no—
291#95—471no—
292#95—471no—
293#95—471no—
294#95C2×D4711yescharacteristic, complemented
295C24—471no—
296C24—471no—
297C24—942no—
298C24—942no—
299C24—942no—
300C24—1881no—
301C24—1881no—
302C24—1881no—
303C24—1881no—
304C24C22×D4711yescharacteristic
305C24C22×D4711yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—942no—
310C2×D4—942no—
311C2×D4—942no—
312C2×D4—1881no—
313C2×D4—1881no—
314C2×D4—1881no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4C22×D4711yescharacteristic
322C22×C4C22×D4711yescharacteristic
323C22×C4C22×D4711yescharacteristic
324C22×C4C22×D4711yescharacteristic
325C22×C4C22×D4711yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—942no—
328C4⋊C4—942no—
329C4⋊C4—1881no—
330C4⋊C4—1881no—
331C4⋊C4—1881no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—474no—
337C22⋊C4—942no—
338C22⋊C4—942no—
339C22⋊C4—942no—
340C22⋊C4—942no—
341C22⋊C4—942no—
342C22⋊C4—1881no—
343C22⋊C4—1881no—
344C22⋊C4—1881no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C22⋊C4—1881no—
349C22⋊C4—1881no—
350C22⋊C4—1881no—
351C42—942no—
352C42—1881no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—472no—
367C23—472no—
368C23—941no—
369C23—941no—
370C23—941no—
371C23—941no—
372C23—941no—
373C23—941no—
374C23—941no—
375C23—941no—
376C23—941no—
377C23—941no—
378C23—941no—
379C23—941no—
380C23—1884no—
381C23—1884no—
382C23—1884no—
383C23—1884no—
384C23—1884no—
385C23—1884no—
386C23—1884no—
387C23#1062535212yes—
388C23C23×D4711yescharacteristic
389D4—44no—
390D4—1884no—
391D4—1884no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—472no—
407C2×C4—941no—
408C2×C4—941no—
409C2×C4—941no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4—941no—
417C2×C4—941no—
418C2×C4—941no—
419C2×C4—941no—
420C2×C4—941no—
421C2×C4—941no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4D4×D4712yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—942no—
440C22—942no—
441C22—942no—
442C22—942no—
443C22—942no—
444C22—942no—
445C22—18816no—
446C22—1881no—
447C22—1881no—
448C22—1881no—
449C22—1881no—
450C22—1881no—
451C22—1881no—
452C22—1881no—
453C22—1881no—
454C22C2×D4×D4711yescharacteristic
455C22#41×D4711yescharacteristic
456C22C2×#1062535211yescharacteristic
457C22#1309406911yescharacteristic
458C22#1309406911yescharacteristic
459C22#1309407011yescharacteristic
460C22#1309407011yescharacteristic
461C4—22no—
462C4—41no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—942no—
467C4—1881no—
468C4—1881no—
469C4—1881no—
470C4—1881no—
471C4—1881no—
472C2—42no—
473C2—81no—
474C2—1882no—
475C2—1882no—
476C2#1568969111yescharacteristic
477C2#1568970911yescharacteristic
478C2#1568971011yescharacteristic
479C2#1568976011yescharacteristic
480C2#1568977011yescharacteristic
481C2#1568979611yescharacteristic
482C2#1568986111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2685
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13094019C2semidirect
3. #15689060C2semidirect
4. #15689046C2semidirect
5. #15689039C2semidirect
6. #15689039C2semidirect
7. #15689038C2semidirect
8. #15689026C2semidirect
9. #15689023C2semidirect
10. #15689016C2semidirect
11. #15689013C2semidirect
12. #15689012C2semidirect
13. #15688978C2semidirect
14. #15688978C2semidirect
15. C47×#394C2semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×C4⋊Dic47C22semidirect
24. C2×Dic47⋊C4C22semidirect
25. C2×Dic47⋊C4C22semidirect
29. C2×C22⋊Dic47C22semidirect
30. C2×C22⋊Dic47C22semidirect
41. C2×C4×Dic47C22semidirect
42. C2×C4×Dic47C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
47. C2×C4⋊C4×C47C22semidirect
50. C2×C22⋊C4×C47C22semidirect
51. C2×C22⋊C4×C47C22semidirect
52. #95×C47C22semidirect
249. #394D47semidirect
257. C47#2685semidirect
269. C2×C4⋊C4C2×D47semidirect
287. C2×C22⋊C4C2×D47semidirect
288. C2×C22⋊C4C2×D47semidirect
294. #95C2×D47semidirect