Finite Group Databasebeta

← #20248964

Subgroups — #20248964

Order 6016.

492 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic94C211yesmaximal, characteristic, complemented
2C2×#13093982C211yesmaximal, characteristic
3#15689056C211yesmaximal, characteristic, complemented
4#15689052C211yesmaximal, characteristic
5#15689044C211yesmaximal, characteristic, complemented
6#15689036C211yesmaximal, characteristic
7#15689015C211yesmaximal, characteristic
8#15689014C211yesmaximal, characteristic
9#15689010C211yesmaximal, characteristic, complemented
10#15689006C211yesmaximal, characteristic, complemented
11#15689004C211yesmaximal, characteristic, complemented
12#15688997C211yesmaximal, characteristic
13#15688994C211yesmaximal, characteristic
14#15688990C211yesmaximal, characteristic, complemented
15C47×#387C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C4×Dic94—24no—
19#13093982—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊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×C4×Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×Dic94—22no—
72C2×Dic94—22no—
73C2×Dic94—22no—
74C4⋊C4×C47—22no—
75C4⋊C4×C47—22no—
76C42×C47—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—22no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—22no—
83C4⋊Dic47—22no—
84C4⋊Dic47—22no—
85C4⋊Dic47—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—22no—
90C4×Dic47—22no—
91C4×Dic47—22no—
92C4×Dic47D414yes—
93C23×C47C2411yescharacteristic
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47#4112yes—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47C2×D412yes—
120C2×C4×C47#4112yes—
121C2×C4×C47#4112yes—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47C2×D412yes—
141C2×Dic47C2×D412yes—
142C2×Dic47#4112yes—
143C4×D47—28no—
144Dic94—28no—
145C22×C47C22×D411yescharacteristic
146C22×C47C2×#4111yescharacteristic
147C22×C47C2×#4111yescharacteristic
148C22×C47C2×#4111yescharacteristic
149C22×C47C2×#4111yescharacteristic
150C22×C472−1+411yescharacteristic
151C22×C472−1+411yescharacteristic
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—22no—
160C4×C47—22no—
161C4×C47—22no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166Dic47—22no—
167Dic47—22no—
168Dic47—22no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173#2599—471nomaximal, Sylow
174C2×C47#52511yescharacteristic
175C2×C47#52511yescharacteristic
176C2×C47#53611yescharacteristic
177C2×C47#55211yescharacteristic
178C2×C47#55211yescharacteristic
179C2×C47#55611yescharacteristic
180C2×C47#55611yescharacteristic
181D47—42no—
182C2×C4×Q8—471no—
183C2×#117—471no—
184#398—471no—
185#397—471no—
186#395—471no—
187#393—471no—
188#388—471no—
189#388—471no—
190#387—471no—
191#387—471no—
192#387—471no—
193#387D4711yescharacteristic, complemented
194#385—471no—
195#385—471no—
196#383—471no—
197C47#259911yescharacteristic, complemented, Sylow
198C22×Q8—471no—
199C23×C4—471no—
200C4×Q8—944no—
201#117—944no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4C2×D4711yescharacteristic
210C2×C4⋊C4C2×D4711yescharacteristic
211C2×C22⋊C4—471no—
212C2×C22⋊C4—471no—
213C2×C22⋊C4—471no—
214C2×C22⋊C4—471no—
215C2×C22⋊C4—471no—
216C2×C22⋊C4—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42—471no—
220C2×C42C2×D4711yescharacteristic
221#95—471no—
222#95—471no—
223#95—471no—
224#95—471no—
225#95—471no—
226#95—471no—
227#95—471no—
228#95—471no—
229#95—471no—
230#95—471no—
231#95C2×D4711yescharacteristic
232#95C2×D4711yescharacteristic
233#95C2×D4711yescharacteristic
234#95C2×D4711yescharacteristic
235C24—471no—
236C2×Q8—942no—
237C2×Q8—942no—
238C2×Q8—942no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—942no—
247C22×C4—942no—
248C22×C4—942no—
249C22×C4C22×D4711yescharacteristic
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252C22×C4C22×D4711yescharacteristic
253C22×C4C22×D4711yescharacteristic
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—942no—
259C4⋊C4—942no—
260C4⋊C4—942no—
261C4⋊C4—942no—
262C4⋊C4—942no—
263C4⋊C4—942no—
264C4⋊C4—942no—
265C22⋊C4—942no—
266C22⋊C4—942no—
267C22⋊C4—942no—
268C22⋊C4—942no—
269C22⋊C4—942no—
270C22⋊C4—942no—
271C42—22no—
272C42—474no—
273C42—942no—
274C42—942no—
275C23—472no—
276C23—941no—
277C23—941no—
278C23—941no—
279C23—941no—
280C23—941no—
281C23—941no—
282C23C23×D4711yescharacteristic
283Q8—948no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—472no—
303C2×C4—472no—
304C2×C4—472no—
305C2×C4—948no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4#1062535012yes—
325C2×C4D4×D4712yes—
326C2×C4#1062535412yes—
327C22—942no—
328C22—942no—
329C22—942no—
330C22—1881no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22C2×D4×D4711yescharacteristic
335C22#41×D4711yescharacteristic
336C22#41×D4711yescharacteristic
337C22C2×#1062535011yescharacteristic
338C22C2×#1062535411yescharacteristic
339C22#1309407111yescharacteristic
340C22#1309407111yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—942no—
349C4—942no—
350C4—942no—
351C4—1881no—
352C4—1881no—
353C4—1881no—
354C4—1881no—
355C2—1882no—
356C2#1568963211yescharacteristic
357C2#1568963611yescharacteristic
358C2#1568969511yescharacteristic
359C2#1568980911yescharacteristic
360C2#1568981111yescharacteristic
361C2#1568984111yescharacteristic
362C2#1568984611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2599
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic94C2semidirect
3. #15689056C2semidirect
5. #15689044C2semidirect
9. #15689010C2semidirect
10. #15689006C2semidirect
11. #15689004C2semidirect
14. #15688990C2semidirect
15. C47×#387C2semidirect
193. #387D47semidirect
197. C47#2599semidirect