Finite Group Databasebeta

← #20250425

Subgroups — #20250425

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#15689059C211yesmaximal, characteristic, complemented
2#15689051C211yesmaximal, characteristic, complemented
3#15689051C211yesmaximal, characteristic, complemented
4#15689048C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689046C211yesmaximal, characteristic, complemented
7#15689017C211yesmaximal, characteristic, complemented
8#15689017C211yesmaximal, characteristic, complemented
9#15689016C211yesmaximal, characteristic, complemented
10#15689016C211yesmaximal, characteristic, complemented
11#15689011C211yesmaximal, characteristic, complemented
12#15689011C211yesmaximal, characteristic, complemented
13#15688979C211yesmaximal, characteristic
14#15688979C211yesmaximal, characteristic
15C47×#379C211yesmaximal, characteristic
16C2×C4⋊Dic47C2211yescharacteristic, complemented
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×C22⋊Dic47C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic, complemented
35C2×C4×Dic47C2211yescharacteristic, complemented
36C47⋊#95C2211yescharacteristic, complemented
37C47⋊#95C2211yescharacteristic, complemented
38C47⋊#95C2211yescharacteristic, complemented
39C47⋊#95C2211yescharacteristic, complemented
40C47⋊#95C2211yescharacteristic, complemented
41C47⋊#95C2211yescharacteristic, complemented
42C47⋊#95C2211yescharacteristic, complemented
43C47⋊#95C2211yescharacteristic, complemented
44C25×C47C2211yescharacteristic
45C2×C22⋊C4×C47C2211yescharacteristic
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C24×C47—22no—
52C24×C47—22no—
53C24×C47—22no—
54C24×C47—41no—
55C24×C47—41no—
56C24×C47—41no—
57C24×C47—41no—
58C24×C47C2311yescharacteristic
59C24×C47C2311yescharacteristic
60C24×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22⋊C4×C47—22no—
74C22⋊C4×C47—22no—
75C22⋊C4×C47—41no—
76C22⋊C4×C47—41no—
77C22⋊C4×C47—41no—
78C22⋊C4×C47—41no—
79C22⋊Dic47—22no—
80C22⋊Dic47—22no—
81C22⋊Dic47—22no—
82C22⋊Dic47—22no—
83C22⋊Dic47—41no—
84C22⋊Dic47—41no—
85C22⋊Dic47—41no—
86C22⋊Dic47—41no—
87C22⋊Dic47—41no—
88C22⋊Dic47—41no—
89C22⋊Dic47—41no—
90C22⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—41no—
93Dic47⋊C4—41no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97C4×Dic47—41no—
98C4×Dic47—41no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—44no—
118C23×C47—44no—
119C23×C47—44no—
120C23×C47—44no—
121C23×C47—44no—
122C23×C47—44no—
123C23×C47—44no—
124C23×C47#4112yes—
125C23×C47#4112yes—
126C23×C47#4112yes—
127C23×C47C2411yescharacteristic
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×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—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—22no—
168C22×C47—22no—
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—22no—
173C22×C47—416no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47C2×#4111yescharacteristic
187C22×C47C2×#4111yescharacteristic
188C22×C47C2×#4111yescharacteristic
189C22×C47H(5,𝔽2)11yescharacteristic
190C22×C47H(5,𝔽2)11yescharacteristic
191C22×C47H(5,𝔽2)11yescharacteristic
192C22×C47H(5,𝔽2)11yescharacteristic
193C4×C47—41no—
194C4×C47—41no—
195C4×C47—41no—
196C4×C47—41no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200Dic47—41no—
201Dic47—41no—
202Dic47—41no—
203Dic47—41no—
204Dic47—41no—
205#2735—471nomaximal, Sylow
206C2×C47—42no—
207C2×C47—42no—
208C2×C47—42no—
209C2×C47#53811yescharacteristic
210C2×C47#53811yescharacteristic
211C2×C47#53811yescharacteristic
212C2×C47#55111yescharacteristic
213C2×C47#55111yescharacteristic
214C2×C47#55111yescharacteristic
215C2×C47#56011yescharacteristic
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#388—471no—
228#379—471no—
229#379—471no—
230#379D4711yescharacteristic
231C47#273511yescharacteristic, complemented, Sylow
232C25C2×D4711yescharacteristic
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C4⋊C4—471no—
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⋊C4C2×D4711yescharacteristic
252C2×C22⋊C4C2×D4711yescharacteristic
253C2×C22⋊C4C2×D4711yescharacteristic
254C2×C22⋊C4C2×D4711yescharacteristic
255C2×C22⋊C4C2×D4711yescharacteristic
256C2×C22⋊C4C2×D4711yescharacteristic
257C2×C42—471no—
258C2×C42—471no—
259#95—471no—
260#95—471no—
261#95—471no—
262#95—471no—
263#95—471no—
264#95—471no—
265#95—471no—
266#95—471no—
267C24—22no—
268C24—22no—
269C24—22no—
270C24—41no—
271C24—41no—
272C24—41no—
273C24—41no—
274C24C22×D4711yescharacteristic
275C24C22×D4711yescharacteristic
276C24C22×D4711yescharacteristic
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—471no—
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C4⋊C4—1881no—
290C4⋊C4—1881no—
291C4⋊C4—1881no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C4⋊C4—1881no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C22⋊C4—942no—
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—1881no—
314C42—1881no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—44no—
334C23—44no—
335C23—44no—
336C23—44no—
337C23—44no—
338C23—44no—
339C23—44no—
340C23#1062535012yes—
341C23#1062535212yes—
342C23#1062535212yes—
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—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
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—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—416no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22C2×#1062535211yescharacteristic
403C22C2×#1062535211yescharacteristic
404C22C2×#1062535011yescharacteristic
405C22#1309406911yescharacteristic
406C22#1309406911yescharacteristic
407C22#1309406911yescharacteristic
408C22#1309406911yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—1881no—
414C4—1881no—
415C4—1881no—
416C4—1881no—
417C4—1881no—
418C4—1881no—
419C4—1881no—
420C4—1881no—
421C2—42no—
422C2—42no—
423C2—42no—
424C2#1568970811yescharacteristic
425C2#1568970811yescharacteristic
426C2#1568971111yescharacteristic
427C2#1568979911yescharacteristic
428C2#1568979911yescharacteristic
429C2#1568980411yescharacteristic
430C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#379C2
hypercenter#379D47
hypocenterC47#2735
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #15689059C2semidirect
2. #15689051C2semidirect
3. #15689051C2semidirect
4. #15689048C2semidirect
5. #15689046C2semidirect
6. #15689046C2semidirect
7. #15689017C2semidirect
8. #15689017C2semidirect
9. #15689016C2semidirect
10. #15689016C2semidirect
11. #15689011C2semidirect
12. #15689011C2semidirect
16. C2×C4⋊Dic47C22semidirect
17. C2×C4⋊Dic47C22semidirect
18. C2×Dic47⋊C4C22semidirect
19. C2×Dic47⋊C4C22semidirect
20. C2×Dic47⋊C4C22semidirect
21. C2×Dic47⋊C4C22semidirect
34. C2×C4×Dic47C22semidirect
35. C2×C4×Dic47C22semidirect
36. C47⋊#95C22semidirect
37. C47⋊#95C22semidirect
38. C47⋊#95C22semidirect
39. C47⋊#95C22semidirect
40. C47⋊#95C22semidirect
41. C47⋊#95C22semidirect
42. C47⋊#95C22semidirect
43. C47⋊#95C22semidirect
231. C47#2735semidirect