Finite Group Databasebeta

← #20246528

Subgroups — #20246528

Order 6016.

688 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×#13093994C211yesmaximal, characteristic
2#15689025C211yesmaximal, characteristic, complemented
3#15689024C211yesmaximal, characteristic, complemented
4#15689023C211yesmaximal, characteristic, complemented
5#15689016C211yesmaximal, characteristic, complemented
6#15689015C211yesmaximal, characteristic, complemented
7#15689014C211yesmaximal, characteristic, complemented
8#15689013C211yesmaximal, characteristic, complemented
9#15689012C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15689001C211yesmaximal, characteristic, complemented
12#15688999C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic, complemented
14#15688978C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic, complemented
21#13093994C418yescomplemented
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×C4×Dic47C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C2×C4⋊C4×C47C2211yescharacteristic, complemented
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C42×C47C2211yescharacteristic, complemented
50#95×C47C2211yescharacteristic, complemented
51#95×C47C2211yescharacteristic, complemented
52C24×C47C2311yescharacteristic
53C23×D47—41no—
54C23×D47—41no—
55C23×D47—41no—
56C23×D47—41no—
57C23×D47—41no—
58C23×D47—41no—
59C23×D47C2×C414yescomplemented
60C23×D47C2311yescharacteristic
61C23×D47C2311yescharacteristic
62C23×D47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—41no—
70C2×C22⋊D47—41no—
71C2×C22⋊D47C2×C414yes—
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188C2×C414yes—
82C2×D188C2×C414yes—
83C2×C4×D47—41no—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C4⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—41no—
89C22⋊C4×C47C2×C414yescomplemented
90C42×C47—41no—
91C22⋊Dic47—41no—
92C22⋊Dic47—41no—
93(C2×D47)⋊C4—41no—
94(C2×D47)⋊C4—41no—
95(C2×D47)⋊C4—41no—
96(C2×D47)⋊C4—41no—
97(C2×D47)⋊C4—41no—
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)⋊C4—41no—
104(C2×D47)⋊C4C2×C414yescomplemented
105(C2×D47)⋊C4C2×C414yescomplemented
106C4⋊Dic47—41no—
107Dic47⋊C4—41no—
108C4×Dic47—41no—
109C4×Dic47—41no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47C22×C412yes—
117C23×C47C2411yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
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—44no—
137C22×D47—44no—
138C22×D47—44no—
139C22×D47—44no—
140C22×D47—44no—
141C22×D47—44no—
142C22×D47—44no—
143C22×D47C22×C412yes—
144C22×D47C22×C412yes—
145C22×D47C22×C412yes—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
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×C47C22×C412yes—
163C2×C4×C47C22×C412yes—
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×Dic47C22×C412yes—
180D188—44no—
181D188—44no—
182C4×D47—44no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—22no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47C23×C411yescharacteristic
191C22×C47H(5,𝔽2)11yescharacteristic
192C22×C47H(5,𝔽2)11yescharacteristic
193C22×C47H(5,𝔽2)11yescharacteristic
194C22×C47H(5,𝔽2)11yescharacteristic
195C22×C47H(5,𝔽2)11yescharacteristic
196C22×C47H(5,𝔽2)11yescharacteristic
197C2×D47—22no—
198C2×D47—22no—
199C2×D47—22no—
200C2×D47—22no—
201C2×D47—22no—
202C2×D47—22no—
203C2×D47—22no—
204C2×D47—22no—
205C2×D47—22no—
206C2×D47—416no—
207C2×D47—41no—
208C2×D47—41no—
209C2×D47—41no—
210C2×D47—41no—
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—22no—
221C4×C47—41no—
222C4×C47—41no—
223C4×C47—41no—
224C4×C47—41no—
225Dic47—22no—
226Dic47—41no—
227Dic47—41no—
228Dic47—41no—
229Dic47—41no—
230#2375—471nomaximal, Sylow
231C2×C47—42no—
232C2×C47#51811yescharacteristic
233C2×C47#51811yescharacteristic
234C2×C47#51811yescharacteristic
235C2×C47#56011yescharacteristic
236C2×C47#56011yescharacteristic
237C2×C47#56011yescharacteristic
238C2×C47H(3,𝔽4)11yescharacteristic
239D47—42no—
240D47—42no—
241D47—42no—
242C2×#120—471no—
243#390—471no—
244#390—471no—
245#390—471no—
246#388—471no—
247#388—471no—
248#388—471no—
249#388—471no—
250#388—471no—
251#388D4711yescharacteristic, complemented
252#386—471no—
253#386—471no—
254#386—471no—
255#379—471no—
256#379—471no—
257C47#237511yescharacteristic, complemented, Sylow
258C25—471no—
259C22×D4—471no—
260C22×D4—471no—
261C22×D4—471no—
262C23×C4—471no—
263#120—478no—
264C2×C4⋊C4—471no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4C2×D4711yescharacteristic, complemented
267C2×C22⋊C4—471no—
268C2×C22⋊C4—471no—
269C2×C22⋊C4—471no—
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⋊C4C2×D4711yescharacteristic
283C2×C22⋊C4C2×D4711yescharacteristic
284C2×C22⋊C4C2×D4711yescharacteristic
285C2×C42—471no—
286C2×C42—471no—
287C2×C42C2×D4711yescharacteristic, complemented
288#95—471no—
289#95—471no—
290#95—471no—
291#95—471no—
292#95C2×D4711yescharacteristic, complemented
293#95C2×D4711yescharacteristic, complemented
294C24—471no—
295C24—471no—
296C24—471no—
297C24—474no—
298C24—1881no—
299C24—1881no—
300C24—1881no—
301C24—1881no—
302C24—1881no—
303C24—1881no—
304C24C22×D4711yescharacteristic
305C2×D4—474no—
306C2×D4—474no—
307C2×D4—474no—
308C2×D4—1881no—
309C2×D4—1881no—
310C2×D4—1881no—
311C2×D4—1881no—
312C2×D4—1881no—
313C2×D4—1881no—
314C22×C4—471no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—1881no—
320C22×C4—1881no—
321C22×C4—1881no—
322C22×C4C22×D4711yescharacteristic
323C22×C4C22×D4711yescharacteristic
324C22×C4C22×D4711yescharacteristic
325C22×C4C22×D4711yescharacteristic
326C22×C4C22×D4711yescharacteristic
327C22×C4C22×D4711yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—1881no—
330C4⋊C4—1881no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—474no—
334C22⋊C4—474no—
335C22⋊C4—1881no—
336C22⋊C4—1881no—
337C22⋊C4—1881no—
338C22⋊C4—1881no—
339C22⋊C4—1881no—
340C22⋊C4—1881no—
341C22⋊C4—1881no—
342C22⋊C4—1881no—
343C22⋊C4—1881no—
344C22⋊C4—1881no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C22⋊C4—1881no—
348C22⋊C4C4×D4714yescomplemented
349C42—41no—
350C42—1881no—
351C42—1881no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—472no—
359C23—472no—
360C23—472no—
361C23—941no—
362C23—941no—
363C23—941no—
364C23—941no—
365C23—941no—
366C23—941no—
367C23—941no—
368C23—941no—
369C23—941no—
370C23—941no—
371C23—941no—
372C23—941no—
373C23—941no—
374C23—941no—
375C23—941no—
376C23—941no—
377C23—941no—
378C23—941no—
379C23—1884no—
380C23—1884no—
381C23—1884no—
382C23—1884no—
383C23—1884no—
384C23—1884no—
385C23—1884no—
386C23C2×C4×D4712yes—
387C23C23×D4711yescharacteristic
388D4—1884no—
389D4—1884no—
390D4—1884no—
391C2×C4—21no—
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—21no—
407C2×C4—472no—
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—1884no—
423C2×C4C2×C4×D4712yes—
424C2×C4C2×C4×D4712yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—942no—
433C22—942no—
434C22—942no—
435C22—942no—
436C22—942no—
437C22—942no—
438C22—942no—
439C22—942no—
440C22—942no—
441C22—18816no—
442C22—1881no—
443C22—1881no—
444C22—1881no—
445C22—1881no—
446C22—1881no—
447C22—1881no—
448C22—1881no—
449C22—1881no—
450C22—1881no—
451C22—1881no—
452C22—1881no—
453C22—1881no—
454C22C22×C4×D4711yescharacteristic
455C22#1309406911yescharacteristic
456C22#1309406911yescharacteristic
457C22#1309407011yescharacteristic
458C22#1309407011yescharacteristic
459C22#1309407011yescharacteristic
460C22#1309407011yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—942no—
468C4—1881no—
469C4—1881no—
470C4—1881no—
471C4—1881no—
472C2—42no—
473C2—1882no—
474C2—1882no—
475C2—1882no—
476C2#1568959511yescharacteristic
477C2#1568959511yescharacteristic
478C2#1568959711yescharacteristic
479C2#1568986111yescharacteristic
480C2#1568986311yescharacteristic
481C2#1568986411yescharacteristic
482C2#1568986511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#388C2
socleC23×C47C24
hypercenter#388D47
hypocenterC47#2375
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #15689025C2semidirect
3. #15689024C2semidirect
4. #15689023C2semidirect
5. #15689016C2semidirect
6. #15689015C2semidirect
7. #15689014C2semidirect
8. #15689013C2semidirect
9. #15689012C2semidirect
10. #15689001C2semidirect
11. #15689001C2semidirect
12. #15688999C2semidirect
13. #15688978C2semidirect
14. #15688978C2semidirect
15. C47×#388C2semidirect
20. C22×C4×D47C22semidirect
21. #13093994C4semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×Dic47⋊C4C22semidirect
36. C2×(C2×D47)⋊C4C22semidirect
37. C2×(C2×D47)⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×C4×Dic47C22semidirect
40. C2×C4×Dic47C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C2×C4⋊C4×C47C22semidirect
49. C2×C42×C47C22semidirect
50. #95×C47C22semidirect
51. #95×C47C22semidirect
59. C23×D47C2×C4semidirect
89. C22⋊C4×C47C2×C4semidirect
104. (C2×D47)⋊C4C2×C4semidirect
105. (C2×D47)⋊C4C2×C4semidirect
251. #388D47semidirect
257. C47#2375semidirect
266. C2×C4⋊C4C2×D47semidirect
287. C2×C42C2×D47semidirect
292. #95C2×D47semidirect
293. #95C2×D47semidirect
348. C22⋊C4C4×D47semidirect