Finite Group Databasebeta

← #20250427

Subgroups — #20250427

Order 6016.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689058C211yesmaximal, characteristic, complemented
2#15689052C211yesmaximal, characteristic, complemented
3#15689051C211yesmaximal, characteristic, complemented
4#15689050C211yesmaximal, characteristic, complemented
5#15689047C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689017C211yesmaximal, characteristic, complemented
8#15689015C211yesmaximal, characteristic, complemented
9#15689014C211yesmaximal, characteristic, complemented
10#15689014C211yesmaximal, characteristic, complemented
11#15689013C211yesmaximal, characteristic, complemented
12#15688978C211yesmaximal, characteristic
13#15688978C211yesmaximal, characteristic
14#15688978C211yesmaximal, characteristic
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic, complemented
18C2×Dic47⋊C4C2211yescharacteristic, complemented
19C2×Dic47⋊C4C2211yescharacteristic, complemented
20C2×Dic47⋊C4C2211yescharacteristic, complemented
21C2×Dic47⋊C4C2211yescharacteristic, complemented
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
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
37C2×C4×Dic47C2211yescharacteristic, complemented
38C47⋊#95C2211yescharacteristic, complemented
39C47⋊#95C2211yescharacteristic, complemented
40C47⋊#95C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C2×C4⋊C4×C47C2211yescharacteristic, complemented
45C2×C22⋊C4×C47C2211yescharacteristic
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic, complemented
49#95×C47C2211yescharacteristic, complemented
50#95×C47C2211yescharacteristic, complemented
51C24×C47C2311yescharacteristic
52C23×D47—22no—
53C23×D47—22no—
54C23×D47—22no—
55C23×D47—41no—
56C23×D47—41no—
57C23×D47—41no—
58C23×D47—41no—
59C23×D47C2311yescharacteristic
60C23×D47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C4⋊C4×C47—41no—
74C22⋊C4×C47—22no—
75C22⋊C4×C47—41no—
76C22⋊C4×C47—41no—
77C42×C47—41no—
78C22⋊Dic47—22no—
79C22⋊Dic47—41no—
80C22⋊Dic47—41no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—22no—
85(C2×D47)⋊C4—41no—
86(C2×D47)⋊C4—41no—
87(C2×D47)⋊C4—41no—
88(C2×D47)⋊C4—41no—
89(C2×D47)⋊C4—41no—
90(C2×D47)⋊C4—41no—
91(C2×D47)⋊C4—41no—
92(C2×D47)⋊C4—41no—
93C4⋊Dic47—41no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98C4×Dic47—41no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47#4112yes—
106C23×C47C2411yescharacteristic
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—44no—
120C22×D47—44no—
121C22×D47—44no—
122C22×D47—44no—
123C22×D47—44no—
124C22×D47—44no—
125C22×D47—44no—
126C22×D47#4112yes—
127C22×D47#4112yes—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
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×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47C2×#4111yescharacteristic
172C22×C47C2×#4111yescharacteristic
173C22×C47C2×#4111yescharacteristic
174C22×C47H(5,𝔽2)11yescharacteristic
175C22×C47H(5,𝔽2)11yescharacteristic
176C22×C47H(5,𝔽2)11yescharacteristic
177C22×C47H(5,𝔽2)11yescharacteristic
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47—22no—
183C2×D47—22no—
184C2×D47—416no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C4×C47—41no—
194C4×C47—41no—
195C4×C47—41no—
196C4×C47—41no—
197C4×C47—41no—
198C4×C47—41no—
199Dic47—41no—
200Dic47—41no—
201Dic47—41no—
202Dic47—41no—
203Dic47—41no—
204Dic47—41no—
205#2735—471nomaximal, Sylow
206C2×C47—42no—
207C2×C47#53811yescharacteristic
208C2×C47#53811yescharacteristic
209C2×C47#53811yescharacteristic
210C2×C47#55111yescharacteristic
211C2×C47#55111yescharacteristic
212C2×C47#55111yescharacteristic
213C2×C47#56011yescharacteristic
214D47—42no—
215D47—42no—
216#399—471no—
217#397—471no—
218#397—471no—
219#397—471no—
220#396—471no—
221#396—471no—
222#388—471no—
223#388—471no—
224#388—471no—
225#388—471no—
226#388—471no—
227#388D4711yescharacteristic, complemented
228#379—471no—
229#379—471no—
230#379—471no—
231C47#273511yescharacteristic, complemented, Sylow
232C25—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C4⋊C4C2×D4711yescharacteristic, complemented
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4—471no—
247C2×C22⋊C4—471no—
248C2×C22⋊C4—471no—
249C2×C22⋊C4—471no—
250C2×C22⋊C4—471no—
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4C2×D4711yescharacteristic
255C2×C22⋊C4C2×D4711yescharacteristic
256C2×C22⋊C4C2×D4711yescharacteristic
257C2×C42—471no—
258C2×C42C2×D4711yescharacteristic, complemented
259#95—471no—
260#95—471no—
261#95—471no—
262#95—471no—
263#95—471no—
264#95—471no—
265#95C2×D4711yescharacteristic, complemented
266#95C2×D4711yescharacteristic, complemented
267C24—471no—
268C24—471no—
269C24—942no—
270C24—942no—
271C24—942no—
272C24—1881no—
273C24—1881no—
274C24—1881no—
275C24—1881no—
276C24C22×D4711yescharacteristic
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—1881no—
291C4⋊C4—1881no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C4⋊C4—1881no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—942no—
299C22⋊C4—942no—
300C22⋊C4—942no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—1881no—
304C22⋊C4—1881no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C22⋊C4—1881no—
309C22⋊C4—1881no—
310C22⋊C4—1881no—
311C22⋊C4—1881no—
312C22⋊C4—1881no—
313C42—41no—
314C42—1881no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—472no—
322C23—472no—
323C23—941no—
324C23—941no—
325C23—941no—
326C23—941no—
327C23—941no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—941no—
332C23—941no—
333C23—941no—
334C23—941no—
335C23—1884no—
336C23—1884no—
337C23—1884no—
338C23—1884no—
339C23—1884no—
340C23—1884no—
341C23—1884no—
342C23#1062535012yes—
343C23C23×D4711yescharacteristic
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—942no—
388C22—942no—
389C22—942no—
390C22—942no—
391C22—942no—
392C22—942no—
393C22—18816no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22—1881no—
398C22—1881no—
399C22—1881no—
400C22—1881no—
401C22—1881no—
402C22#41×D4711yescharacteristic
403C22#41×D4711yescharacteristic
404C22C2×#1062535011yescharacteristic
405C22#1309406911yescharacteristic
406C22#1309406911yescharacteristic
407C22#1309407011yescharacteristic
408C22#1309407011yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—1881no—
416C4—1881no—
417C4—1881no—
418C4—1881no—
419C4—1881no—
420C4—1881no—
421C2—42no—
422C2—1882no—
423C2—1882no—
424C2#1568970611yescharacteristic
425C2#1568970711yescharacteristic
426C2#1568971211yescharacteristic
427C2#1568979711yescharacteristic
428C2#1568980111yescharacteristic
429C2#1568980211yescharacteristic
430C2#1568986111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#388C2
hypercenter#388D47
hypocenterC47#2735
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #15689058C2semidirect
2. #15689052C2semidirect
3. #15689051C2semidirect
4. #15689050C2semidirect
5. #15689047C2semidirect
6. #15689046C2semidirect
7. #15689017C2semidirect
8. #15689015C2semidirect
9. #15689014C2semidirect
10. #15689014C2semidirect
11. #15689013C2semidirect
15. C47×#388C2semidirect
17. C2×C4⋊Dic47C22semidirect
18. C2×Dic47⋊C4C22semidirect
19. C2×Dic47⋊C4C22semidirect
20. C2×Dic47⋊C4C22semidirect
21. C2×Dic47⋊C4C22semidirect
37. C2×C4×Dic47C22semidirect
38. C47⋊#95C22semidirect
39. C47⋊#95C22semidirect
40. C47⋊#95C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
44. C2×C4⋊C4×C47C22semidirect
48. C2×C42×C47C22semidirect
49. #95×C47C22semidirect
50. #95×C47C22semidirect
227. #388D47semidirect
231. C47#2735semidirect
238. C2×C4⋊C4C2×D47semidirect
258. C2×C42C2×D47semidirect
265. #95C2×D47semidirect
266. #95C2×D47semidirect