Finite Group Databasebeta

← #20250613

Subgroups — #20250613

Order 6016.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689065C211yesmaximal, characteristic, complemented
2#15689051C211yesmaximal, characteristic, complemented
3#15689048C211yesmaximal, characteristic, complemented
4#15689046C211yesmaximal, characteristic, complemented
5#15689037C211yesmaximal, characteristic, complemented
6#15689026C211yesmaximal, characteristic, complemented
7#15689011C211yesmaximal, characteristic, complemented
8#15689003C211yesmaximal, characteristic, complemented
9#15689003C211yesmaximal, characteristic, complemented
10#15689003C211yesmaximal, characteristic, complemented
11#15689003C211yesmaximal, characteristic, complemented
12#15688998C211yesmaximal, characteristic, complemented
13#15688990C211yesmaximal, characteristic, complemented
14#15688984C211yesmaximal, characteristic, complemented
15C47×#392C211yesmaximal, characteristic
16C23×Dic47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C22×D4×C47C2211yescharacteristic
45C22×D4×C47C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C24×C47C2311yescharacteristic
52C24×C47C2311yescharacteristic
53C24×C47C2311yescharacteristic
54C2×D4×C47—22no—
55C2×D4×C47—22no—
56C2×D4×C47—22no—
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47—41no—
60C2×D4×C47—41no—
61C2×D4×C47—41no—
62C2×D4×C47—41no—
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47—22no—
68C22×Dic47—41no—
69C22×Dic47—41no—
70C22×Dic47—41no—
71C22×Dic47—41no—
72C22×Dic47—41no—
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22⋊C4×C47—22no—
82C22⋊C4×C47—41no—
83C22⋊C4×C47—41no—
84C22⋊Dic47—22no—
85C22⋊Dic47—41no—
86C22⋊Dic47—41no—
87C22⋊Dic47—41no—
88C22⋊Dic47—41no—
89C22⋊Dic47—41no—
90C22⋊Dic47—41no—
91C22⋊Dic47—41no—
92C22⋊Dic47—41no—
93C22⋊Dic47—41no—
94C4⋊Dic47—41no—
95C4⋊Dic47—41no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98C4×Dic47—22no—
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—21no—
118C23×C47#4112yes—
119C23×C47#4112yes—
120C23×C47C2411yescharacteristic
121D4×C47—44no—
122D4×C47—44no—
123D4×C47—44no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
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#4112yes—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—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—44no—
161C2×Dic47—44no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
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×C47C2×#4111yescharacteristic
184C22×C47C2×#4111yescharacteristic
185C22×C47C2×#4111yescharacteristic
186C22×C47H(5,𝔽2)11yescharacteristic
187C22×C47H(5,𝔽2)11yescharacteristic
188C22×C47H(5,𝔽2)11yescharacteristic
189C22×C47H(5,𝔽2)11yescharacteristic
190C4×C47—22no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194Dic47—41no—
195Dic47—41no—
196Dic47—41no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200Dic47—41no—
201Dic47—41no—
202#2749—471nomaximal, Sylow
203C2×C47—42no—
204C2×C47—42no—
205C2×C47—81no—
206C2×C47#53811yescharacteristic
207C2×C47#53811yescharacteristic
208C2×C47#54011yescharacteristic
209C2×C47#55111yescharacteristic
210C2×C47#55111yescharacteristic
211C2×C47#55311yescharacteristic
212C2×C47#56011yescharacteristic
213#400—471no—
214#397—471no—
215#397—471no—
216#396—471no—
217#394—471no—
218#392D4711yescharacteristic
219#390—471no—
220#388—471no—
221#386—471no—
222#386—471no—
223#386—471no—
224#386—471no—
225#385—471no—
226#383—471no—
227#381—471no—
228C47#274911yescharacteristic, complemented, Sylow
229C22×D4C2×D4711yescharacteristic
230C22×D4C2×D4711yescharacteristic
231C22×D4C2×D4711yescharacteristic
232C23×C4—471no—
233C23×C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C22⋊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⋊C4C2×D4711yescharacteristic
249C2×C22⋊C4C2×D4711yescharacteristic
250C2×C22⋊C4C2×D4711yescharacteristic
251C2×C42—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95—471no—
258#95—471no—
259#95—471no—
260#95—471no—
261#95—471no—
262#95—471no—
263#95C2×D4711yescharacteristic
264C24C22×D4711yescharacteristic
265C24C22×D4711yescharacteristic
266C24C22×D4711yescharacteristic
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—942no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4—1881no—
288C22×C4—1881no—
289C22×C4—1881no—
290C22×C4C22×D4711yescharacteristic
291C22×C4C22×D4711yescharacteristic
292C22×C4C22×D4711yescharacteristic
293C22×C4C22×D4711yescharacteristic
294C4⋊C4—1881no—
295C4⋊C4—1881no—
296C4⋊C4—1881no—
297C4⋊C4—1881no—
298C22⋊C4—22no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—942no—
302C22⋊C4—1881no—
303C22⋊C4—1881no—
304C22⋊C4—1881no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C22⋊C4—1881no—
309C22⋊C4—1881no—
310C22⋊C4—1881no—
311C42—942no—
312C23—21no—
313C23—21no—
314C23—21no—
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#1062535212yes—
332C23#1062535212yes—
333C23C23×D4711yescharacteristic
334D4—44no—
335D4—44no—
336D4—44no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
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—1884no—
373C2×C4—1884no—
374C2×C4#1062535212yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22C2×#1062535211yescharacteristic
397C22C2×#1062535211yescharacteristic
398C22C2×#1062535211yescharacteristic
399C22#1309406911yescharacteristic
400C22#1309406911yescharacteristic
401C22#1309406911yescharacteristic
402C22#1309407011yescharacteristic
403C4—22no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—1881no—
408C4—1881no—
409C4—1881no—
410C4—1881no—
411C4—1881no—
412C4—1881no—
413C4—1881no—
414C4—1881no—
415C2—42no—
416C2—42no—
417C2—81no—
418C2#1568970811yescharacteristic
419C2#1568971011yescharacteristic
420C2#1568972711yescharacteristic
421C2#1568980411yescharacteristic
422C2#1568980411yescharacteristic
423C2#1568982511yescharacteristic
424C2#1568986111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2749
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #15689065C2semidirect
2. #15689051C2semidirect
3. #15689048C2semidirect
4. #15689046C2semidirect
5. #15689037C2semidirect
6. #15689026C2semidirect
7. #15689011C2semidirect
8. #15689003C2semidirect
9. #15689003C2semidirect
10. #15689003C2semidirect
11. #15689003C2semidirect
12. #15688998C2semidirect
13. #15688990C2semidirect
14. #15688984C2semidirect
228. C47#2749semidirect