Finite Group Databasebeta

← #20249198

Subgroups — #20249198

Order 6016.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094002C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D47C211yesmaximal, characteristic
3#15689059C211yesmaximal, characteristic, complemented
4#15689058C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689045C211yesmaximal, characteristic, complemented
8#15689036C211yesmaximal, characteristic, complemented
9#15689035C211yesmaximal, characteristic, complemented
10#15688997C211yesmaximal, characteristic, complemented
11#15688994C211yesmaximal, characteristic, complemented
12#15688980C211yesmaximal, characteristic, complemented
13#15688978C211yesmaximal, characteristic
14#15688978C211yesmaximal, characteristic
15C47×#396C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×Dic94C2211yescharacteristic, complemented
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094002—24no—
21C2×C4⋊Dic47C2211yescharacteristic, complemented
22C2×C4⋊Dic47C2211yescharacteristic, complemented
23C2×Dic47⋊C4C2211yescharacteristic, complemented
24C2×Dic47⋊C4C2211yescharacteristic, complemented
25C2×Dic47⋊C4C2211yescharacteristic, complemented
26C2×Dic47⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
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
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C22⋊C4×D47—24no—
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C47⋊#95C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C2×C4⋊C4×C47C2211yescharacteristic, complemented
47C2×C4⋊C4×C47C2211yescharacteristic, complemented
48C2×C4⋊C4×C47C2211yescharacteristic, complemented
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic, complemented
53C24×C47C2311yescharacteristic
54C23×D47—22no—
55C23×D47—22no—
56C23×D47—41no—
57C23×D47—41no—
58C23×D47—41no—
59C23×D47—41no—
60C23×D47Q814yescomplemented
61C23×D47C2311yescharacteristic
62C23×D47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C2×C4×D47—22no—
76C2×C4×D47—41no—
77C2×C4×D47—41no—
78C2×C4×D47—41no—
79C2×C4×D47—41no—
80C2×C4×D47D414yes—
81C2×Dic94—22no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C4⋊C4×C47—22no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47—41no—
89C22⋊C4×C47—41no—
90C22⋊Dic47—22no—
91C22⋊Dic47—41no—
92C22⋊Dic47—41no—
93(C2×D47)⋊C4—22no—
94(C2×D47)⋊C4—22no—
95(C2×D47)⋊C4—22no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—41no—
100(C2×D47)⋊C4—41no—
101(C2×D47)⋊C4—41no—
102(C2×D47)⋊C4—41no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105Dic47⋊C4—22no—
106Dic47⋊C4—22no—
107Dic47⋊C4—41no—
108Dic47⋊C4—41no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47C2×Q812yes—
116C23×C47C2411yescharacteristic
117C22×D47—21no—
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—28no—
128C22×D47—44no—
129C22×D47—44no—
130C22×D47—44no—
131C22×D47—44no—
132C22×D47—44no—
133C22×D47—44no—
134C22×D47C2×D412yes—
135C22×D47C2×Q812yes—
136C22×D47C2×Q812yes—
137C22×D47#4112yes—
138C2×C4×C47—21no—
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×C47—21no—
155C2×C4×C47C2×D412yes—
156C2×Dic47—21no—
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×Dic47—21no—
173C2×Dic47C2×D412yes—
174C4×D47—44no—
175C4×D47—44no—
176Dic94—44no—
177C22×C47—22no—
178C22×C47—22no—
179C22×C47—22no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47C22×D411yescharacteristic
185C22×C47C22×Q811yescharacteristic
186C22×C47C2×#4111yescharacteristic
187C22×C47H(5,𝔽2)11yescharacteristic
188C22×C47H(5,𝔽2)11yescharacteristic
189C22×C47H(5,𝔽2)11yescharacteristic
190C22×C47H(5,𝔽2)11yescharacteristic
191C2×D47—22no—
192C2×D47—22no—
193C2×D47—22no—
194C2×D47—22no—
195C2×D47—22no—
196C2×D47—22no—
197C2×D47—22no—
198C2×D47—22no—
199C2×D47—22no—
200C2×D47—416no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47—41no—
204C2×D47—41no—
205C2×D47C22⋊Q814yes—
206C4×C47—22no—
207C4×C47—41no—
208C4×C47—41no—
209C4×C47—41no—
210C4×C47—41no—
211C4×C47—41no—
212Dic47—22no—
213Dic47—41no—
214Dic47—41no—
215Dic47—41no—
216Dic47—41no—
217Dic47—41no—
218#2626—471nomaximal, Sylow
219C2×C47—42no—
220C2×C47C2×C22⋊Q811yescharacteristic
221C2×C47#53411yescharacteristic
222C2×C47#53511yescharacteristic
223C2×C47#53811yescharacteristic
224C2×C47#53811yescharacteristic
225C2×C47#54311yescharacteristic
226C2×C47#54311yescharacteristic
227D47—24no—
228D47—42no—
229C2×C22⋊Q8—471no—
230C22×C22⋊C4—471no—
231#399—471no—
232#399—471no—
233#396—471no—
234#396—471no—
235#396—471no—
236#396D4711yescharacteristic, complemented
237#393—471no—
238#393—471no—
239#385—471no—
240#385—471no—
241#380—471no—
242#379—471no—
243#379—471no—
244C47#262611yescharacteristic, complemented, Sylow
245C25—471no—
246C22×Q8—471no—
247C23×C4—471no—
248C23×C4—471no—
249C22⋊Q8—944no—
250C2×C4⋊C4—471no—
251C2×C4⋊C4—471no—
252C2×C4⋊C4—471no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4C2×D4711yescharacteristic, complemented
257C2×C4⋊C4C2×D4711yescharacteristic, complemented
258C2×C4⋊C4C2×D4711yescharacteristic, complemented
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—471no—
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—471no—
270C2×C22⋊C4—471no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—944no—
273C2×C22⋊C4C2×D4711yescharacteristic
274C2×C22⋊C4C2×D4711yescharacteristic
275C2×C22⋊C4C2×D4711yescharacteristic
276#95—471no—
277#95—471no—
278#95—471no—
279#95—471no—
280#95—471no—
281#95C2×D4711yescharacteristic, complemented
282C24—471no—
283C24—471no—
284C24—474no—
285C24—942no—
286C24—942no—
287C24—1881no—
288C24—1881no—
289C24—1881no—
290C24—1881no—
291C24C22×D4711yescharacteristic
292C2×Q8—942no—
293C2×Q8—1881no—
294C2×Q8—1881no—
295C22×C4—471no—
296C22×C4—474no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—471no—
300C22×C4—471no—
301C22×C4—471no—
302C22×C4—942no—
303C22×C4—1881no—
304C22×C4—1881no—
305C22×C4—1881no—
306C22×C4—1881no—
307C22×C4C22×D4711yescharacteristic
308C22×C4C22×D4711yescharacteristic
309C22×C4C22×D4711yescharacteristic
310C22×C4C22×D4711yescharacteristic
311C22×C4C22×D4711yescharacteristic
312C22×C4C22×D4711yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—942no—
317C4⋊C4—942no—
318C4⋊C4—1881no—
319C4⋊C4—1881no—
320C4⋊C4—1881no—
321C4⋊C4—1881no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—942no—
326C22⋊C4—942no—
327C22⋊C4—942no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—942no—
331C22⋊C4—942no—
332C22⋊C4—1881no—
333C22⋊C4—1881no—
334C22⋊C4—1881no—
335C22⋊C4—1881no—
336C22⋊C4—1881no—
337C22⋊C4—1881no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—472no—
345C23—472no—
346C23—472no—
347C23—472no—
348C23—948no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—941no—
357C23—941no—
358C23—941no—
359C23—1884no—
360C23—1884no—
361C23—1884no—
362C23—1884no—
363C23—1884no—
364C23—1884no—
365C23Q8×D4712yes—
366C23C23×D4711yescharacteristic
367Q8—1884no—
368C2×C4—21no—
369C2×C4—21no—
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—941no—
387C2×C4—941no—
388C2×C4—941no—
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—1884no—
404C2×C4—1884no—
405C2×C4D4×D4712yes—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—474no—
414C22—942no—
415C22—942no—
416C22—942no—
417C22—942no—
418C22—942no—
419C22—942no—
420C22—942no—
421C22—942no—
422C22—942no—
423C22—18816no—
424C22—1881no—
425C22—1881no—
426C22—1881no—
427C22—1881no—
428C22C2×D4×D4711yescharacteristic
429C22C2×Q8×D4711yescharacteristic
430C22#41×D4711yescharacteristic
431C22#1309406911yescharacteristic
432C22#1309406911yescharacteristic
433C22#1309407011yescharacteristic
434C22#1309407011yescharacteristic
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—942no—
442C4—1881no—
443C4—1881no—
444C4—1881no—
445C4—1881no—
446C4—1881no—
447C2—42no—
448C2—944no—
449C2—1882no—
450C2C22⋊Q8×D4711yescharacteristic
451C2#1568968111yescharacteristic
452C2#1568968911yescharacteristic
453C2#1568970511yescharacteristic
454C2#1568971211yescharacteristic
455C2#1568974811yescharacteristic
456C2#1568974811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
3. #15689059C2semidirect
4. #15689058C2semidirect
5. #15689046C2semidirect
6. #15689045C2semidirect
7. #15689045C2semidirect
8. #15689036C2semidirect
9. #15689035C2semidirect
10. #15688997C2semidirect
11. #15688994C2semidirect
12. #15688980C2semidirect
15. C47×#396C2semidirect
17. C22×Dic94C22semidirect
21. C2×C4⋊Dic47C22semidirect
22. C2×C4⋊Dic47C22semidirect
23. C2×Dic47⋊C4C22semidirect
24. C2×Dic47⋊C4C22semidirect
25. C2×Dic47⋊C4C22semidirect
26. C2×Dic47⋊C4C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C47⋊#95C22semidirect
45. C47⋊#95C22semidirect
46. C2×C4⋊C4×C47C22semidirect
47. C2×C4⋊C4×C47C22semidirect
48. C2×C4⋊C4×C47C22semidirect
52. #95×C47C22semidirect
60. C23×D47Q8semidirect
236. #396D47semidirect
244. C47#2626semidirect
256. C2×C4⋊C4C2×D47semidirect
257. C2×C4⋊C4C2×D47semidirect
258. C2×C4⋊C4C2×D47semidirect
281. #95C2×D47semidirect