Finite Group Databasebeta

← #20246236

Subgroups — #20246236

Order 6016.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093982C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D47C211yesmaximal, characteristic
3C2×C22⋊C4×D47C211yesmaximal, characteristic
4#15689017C211yesmaximal, characteristic, complemented
5#15689016C211yesmaximal, characteristic, complemented
6#15689011C211yesmaximal, characteristic, complemented
7#15688997C211yesmaximal, characteristic, complemented
8#15688994C211yesmaximal, characteristic, complemented
9#15688985C211yesmaximal, characteristic, complemented
10#15688982C211yesmaximal, characteristic, complemented
11#15688978C211yesmaximal, characteristic
12C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
13C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21#13093982—24no—
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
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
36C22⋊C4×D47—24no—
37C22⋊C4×D47C418yescomplemented
38C2×C4×Dic47C2211yescharacteristic, complemented
39C2×C4×Dic47C2211yescharacteristic, complemented
40C2×C4×Dic47C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C2×C4⋊C4×C47C2211yescharacteristic, complemented
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C42×C47C2211yescharacteristic, complemented
52#95×C47C2211yescharacteristic, complemented
53#95×C47C2211yescharacteristic, complemented
54C24×C47C2311yescharacteristic
55C23×D47—22no—
56C23×D47—22no—
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—41no—
60C23×D47—41no—
61C23×D47C2×C414yes—
62C23×D47C2311yescharacteristic
63C23×D47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×C4×D47—22no—
80C2×C4×D47—22no—
81C2×C4×D47—22no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C2×C4×D47C2×C414yescomplemented
87C2×C4×D47C2×C414yescomplemented
88C4⋊C4×C47—22no—
89C22⋊C4×C47—22no—
90C22⋊C4×C47—41no—
91C22⋊C4×C47C2×C414yescomplemented
92C42×C47—41no—
93C22⋊Dic47—22no—
94C22⋊Dic47—41no—
95C22⋊Dic47C2×C414yescomplemented
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4C2×C414yes—
102(C2×D47)⋊C4C2×C414yes—
103(C2×D47)⋊C4D414yes—
104C4⋊Dic47—22no—
105Dic47⋊C4—41no—
106Dic47⋊C4—41no—
107C4×Dic47—22no—
108C4×Dic47—22no—
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—28no—
127C22×D47—28no—
128C22×D47—44no—
129C22×D47—44no—
130C22×D47—44no—
131C22×D47—44no—
132C22×D47—44no—
133C22×D47C22×C412yes—
134C22×D47C22×C412yes—
135C22×D47C2×D412yes—
136C22×D47#4112yes—
137C22×D47#4112yes—
138C22×D47#4112yes—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
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×C47C22×C412yes—
155C2×C4×C47C22×C412yes—
156C2×C4×C47C2×D412yes—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47C22×C412yes—
173C2×Dic47C22×C412yes—
174C2×Dic47C2×D412yes—
175C4×D47—28no—
176C4×D47—44no—
177C4×D47—44no—
178C4×D47—44no—
179C22×C47—22no—
180C22×C47—22no—
181C22×C47—22no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47C23×C411yescharacteristic
187C22×C47C22×D411yescharacteristic
188C22×C47C2×#4111yescharacteristic
189C22×C47C2×#4111yescharacteristic
190C22×C47C2×#4111yescharacteristic
191C22×C47H(5,𝔽2)11yescharacteristic
192C22×C47H(5,𝔽2)11yescharacteristic
193C2×D47—22no—
194C2×D47—22no—
195C2×D47—22no—
196C2×D47—22no—
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—416no—
206C2×D47#11714yescomplemented
207C2×D47C4×D414yes—
208C4×C47—22no—
209C4×C47—22no—
210C4×C47—22no—
211C4×C47—41no—
212C4×C47—41no—
213C4×C47—41no—
214Dic47—22no—
215Dic47—22no—
216Dic47—22no—
217Dic47—41no—
218Dic47—41no—
219Dic47—41no—
220#2342—471nomaximal, Sylow
221C2×C47—42no—
222C2×C47C2×#11711yescharacteristic
223C2×C47C2×C4×D411yescharacteristic
224C2×C47#51811yescharacteristic
225C2×C47#54611yescharacteristic
226C2×C47#54611yescharacteristic
227C2×C47#55111yescharacteristic
228C2×C47#55111yescharacteristic
229D47—24no—
230D47—24no—
231C2×#117—471no—
232C22×C22⋊C4—471no—
233C22×C22⋊C4—471no—
234#388—471no—
235#388—471no—
236#388—471no—
237#388D4711yescharacteristic, complemented
238#385—471no—
239#385—471no—
240#381—471no—
241#380—471no—
242#379—471no—
243C4×C22⋊C4—471no—
244C4×C22⋊C4—471no—
245C4×C22⋊C4—471no—
246C47#234211yescharacteristic, complemented, Sylow
247C25—471no—
248C23×C4—471no—
249C23×C4—471no—
250C23×C4—471no—
251C23×C4—471no—
252#117—944no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4C2×D4711yescharacteristic, complemented
257C2×C22⋊C4—471no—
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—478no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—471no—
265C2×C22⋊C4—471no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4—471no—
269C2×C22⋊C4—944no—
270C2×C22⋊C4C2×D4711yescharacteristic
271C2×C22⋊C4C2×D4711yescharacteristic
272C2×C22⋊C4C2×D4711yescharacteristic
273C2×C42—471no—
274C2×C42—471no—
275C2×C42—471no—
276C2×C42C2×D4711yescharacteristic, complemented
277#95—471no—
278#95—471no—
279#95—471no—
280#95—471no—
281#95—471no—
282#95—471no—
283#95C2×D4711yescharacteristic, complemented
284#95C2×D4711yescharacteristic, complemented
285C24—471no—
286C24—471no—
287C24—474no—
288C24—942no—
289C24—942no—
290C24—942no—
291C24—942no—
292C24—1881no—
293C24—1881no—
294C24C22×D4711yescharacteristic
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—474no—
299C22×C4—474no—
300C22×C4—471no—
301C22×C4—471no—
302C22×C4—471no—
303C22×C4—942no—
304C22×C4—942no—
305C22×C4—942no—
306C22×C4—942no—
307C22×C4—942no—
308C22×C4—942no—
309C22×C4—1881no—
310C22×C4—1881no—
311C22×C4—1881no—
312C22×C4—1881no—
313C22×C4C22×D4711yescharacteristic
314C22×C4C22×D4711yescharacteristic
315C22×C4C22×D4711yescharacteristic
316C22×C4C22×D4711yescharacteristic
317C22×C4C22×D4711yescharacteristic
318C22×C4C22×D4711yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—942no—
321C4⋊C4—1881no—
322C4⋊C4—1881no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—474no—
326C22⋊C4—474no—
327C22⋊C4—474no—
328C22⋊C4—474no—
329C22⋊C4—942no—
330C22⋊C4—942no—
331C22⋊C4—942no—
332C22⋊C4—942no—
333C22⋊C4—942no—
334C22⋊C4—942no—
335C22⋊C4—1881no—
336C22⋊C4C4×D4714yescomplemented
337C42—41no—
338C42—942no—
339C42—942no—
340C42—1881no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—472no—
348C23—472no—
349C23—472no—
350C23—472no—
351C23—472no—
352C23—472no—
353C23—948no—
354C23—948no—
355C23—941no—
356C23—941no—
357C23—941no—
358C23—941no—
359C23—941no—
360C23—941no—
361C23—941no—
362C23—941no—
363C23—1884no—
364C23—1884no—
365C23—1884no—
366C23—1884no—
367C23—1884no—
368C23C2×C4×D4712yes—
369C23C23×D4711yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—472no—
386C2×C4—472no—
387C2×C4—472no—
388C2×C4—948no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—941no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—941no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—941no—
403C2×C4—941no—
404C2×C4—1884no—
405C2×C4—1884no—
406C2×C4—1884no—
407C2×C4C2×C4×D4712yes—
408C2×C4C2×C4×D4712yes—
409C2×C4D4×D4712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—474no—
418C22—474no—
419C22—942no—
420C22—942no—
421C22—942no—
422C22—942no—
423C22—942no—
424C22—942no—
425C22—942no—
426C22—942no—
427C22—942no—
428C22—942no—
429C22—942no—
430C22—942no—
431C22—18816no—
432C22C22×C4×D4711yescharacteristic
433C22C2×D4×D4711yescharacteristic
434C22#41×D4711yescharacteristic
435C22#41×D4711yescharacteristic
436C22#41×D4711yescharacteristic
437C22#1309406911yescharacteristic
438C22#1309407011yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—942no—
446C4—942no—
447C4—942no—
448C4—1881no—
449C4—1881no—
450C4—1881no—
451C2—42no—
452C2—944no—
453C2—944no—
454C2#117×D4711yescharacteristic
455C2C4×D4×D4711yescharacteristic
456C2#1568959511yescharacteristic
457C2#1568976211yescharacteristic
458C2#1568976611yescharacteristic
459C2#1568979811yescharacteristic
460C2#1568980111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#388C2
socleC23×C47C24
hypercenter#388D47
hypocenterC47#2342
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#13093982C2semidirect
4. #15689017C2semidirect
5. #15689016C2semidirect
6. #15689011C2semidirect
7. #15688997C2semidirect
8. #15688994C2semidirect
9. #15688985C2semidirect
10. #15688982C2semidirect
12. C4×(C2×D47)⋊C4C2semidirect
13. C4×(C2×D47)⋊C4C2semidirect
14. #15688970C2semidirect
15. C47×#388C2semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×Dic47⋊C4C22semidirect
24. C2×Dic47⋊C4C22semidirect
37. C22⋊C4×D47C4semidirect
38. C2×C4×Dic47C22semidirect
39. C2×C4×Dic47C22semidirect
40. C2×C4×Dic47C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C2×C4⋊C4×C47C22semidirect
51. C2×C42×C47C22semidirect
52. #95×C47C22semidirect
53. #95×C47C22semidirect
86. C2×C4×D47C2×C4semidirect
87. C2×C4×D47C2×C4semidirect
91. C22⋊C4×C47C2×C4semidirect
95. C22⋊Dic47C2×C4semidirect
206. C2×D47#117semidirect
237. #388D47semidirect
246. C47#2342semidirect
256. C2×C4⋊C4C2×D47semidirect
276. C2×C42C2×D47semidirect
283. #95C2×D47semidirect
284. #95C2×D47semidirect
336. C22⋊C4C4×D47semidirect