Finite Group Databasebeta

← #20247768

Subgroups — #20247768

Order 6016.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689065C211yesmaximal, characteristic, complemented
2#15689064C211yesmaximal, characteristic, complemented
3#15689064C211yesmaximal, characteristic, complemented
4#15689010C211yesmaximal, characteristic, complemented
5#15689008C211yesmaximal, characteristic, complemented
6#15689006C211yesmaximal, characteristic, complemented
7#15688997C211yesmaximal, characteristic
8#15688997C211yesmaximal, characteristic
9#15688990C211yesmaximal, characteristic, complemented
10#15688985C211yesmaximal, characteristic
11#15688985C211yesmaximal, characteristic
12#15688982C211yesmaximal, characteristic
13#15688970C211yesmaximal, characteristic
14#95×D47C211yesmaximal, characteristic
15C47×#401C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C47⋊#95C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44#95×C47C2211yescharacteristic
45#95×C47C2211yescharacteristic
46#95×C47C2211yescharacteristic
47#95×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C23×D47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C2×C4×D47—22no—
67C2×C4×D47—22no—
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79C4⋊Dic47—22no—
80C4⋊Dic47—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—41no—
83Dic47⋊C4—41no—
84Dic47⋊C4—41no—
85C4×Dic47—22no—
86C4×Dic47—41no—
87C23×C47C2411yescharacteristic
88C22×D47—21no—
89C22×D47—21no—
90C22×D47—21no—
91C22×D47—21no—
92C22×D47#4112yes—
93C22×D47#4112yes—
94C22×D47#4112yes—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
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×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
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#4112yes—
136C2×Dic47#4112yes—
137C4×D47—44no—
138C4×D47—44no—
139C4×D47—44no—
140C22×C47C2×#4111yescharacteristic
141C22×C47C2×#4111yescharacteristic
142C22×C47C2×#4111yescharacteristic
143C22×C47C2×#4111yescharacteristic
144C22×C47C2×#4111yescharacteristic
145C22×C47H(5,𝔽2)11yescharacteristic
146C22×C472−1+411yescharacteristic
147C2×D47—22no—
148C2×D47—22no—
149C2×D47—22no—
150C2×D47—22no—
151C2×D47—22no—
152C2×D47—22no—
153C2×D47#12614yes—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161Dic47—22no—
162Dic47—22no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168#2493—471nomaximal, Sylow
169C2×C47C2×#12611yescharacteristic
170C2×C47#52911yescharacteristic
171C2×C47#53911yescharacteristic
172C2×C47#55111yescharacteristic
173C2×C47#55111yescharacteristic
174C2×C47#55211yescharacteristic
175C2×C47#55211yescharacteristic
176D47—24no—
177#401D4711yescharacteristic, complemented
178#400—471no—
179#400—471no—
180#400—471no—
181#387—471no—
182#387—471no—
183#387—471no—
184#385—471no—
185#385—471no—
186#383—471no—
187#381—471no—
188#381—471no—
189#380—471no—
190C4×C22⋊C4—471no—
191C2×#95—471no—
192C47#249311yescharacteristic, complemented, Sylow
193C23×C4—471no—
194C23×C4—471no—
195C23×C4—471no—
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C22⋊C4—471no—
203C2×C22⋊C4—471no—
204C2×C22⋊C4—471no—
205C2×C22⋊C4—471no—
206C2×C42—471no—
207C2×C42—471no—
208#95—471no—
209#95—471no—
210#95—471no—
211#95—471no—
212#95—471no—
213#95—471no—
214#95—471no—
215#95—471no—
216#95—471no—
217#95—471no—
218#95—471no—
219#95—471no—
220#95—471no—
221#95C2×D4711yescharacteristic
222#95C2×D4711yescharacteristic
223#95C2×D4711yescharacteristic
224#95C2×D4711yescharacteristic
225#95C2×D4711yescharacteristic
226#95C2×D4711yescharacteristic
227#95C2×D4711yescharacteristic
228C24—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—942no—
237C22×C4—942no—
238C22×C4—942no—
239C22×C4—942no—
240C22×C4—942no—
241C22×C4—942no—
242C22×C4—942no—
243C22×C4—1881no—
244C22×C4—1881no—
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250C22×C4C22×D4711yescharacteristic
251C22×C4C22×D4711yescharacteristic
252C4⋊C4—942no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C22⋊C4—942no—
259C22⋊C4—942no—
260C22⋊C4—942no—
261C22⋊C4—942no—
262C42—942no—
263C42—1881no—
264C23—472no—
265C23—472no—
266C23—472no—
267C23—941no—
268C23—941no—
269C23—941no—
270C23—941no—
271C23C23×D4711yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
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—472no—
294C2×C4—472no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
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—1884no—
315C2×C4—1884no—
316C2×C4—1884no—
317C22—474no—
318C22—942no—
319C22—942no—
320C22—942no—
321C22—942no—
322C22—942no—
323C22—942no—
324C22#41×D4711yescharacteristic
325C22#41×D4711yescharacteristic
326C22#41×D4711yescharacteristic
327C22#41×D4711yescharacteristic
328C22#41×D4711yescharacteristic
329C22#1309407011yescharacteristic
330C22#1309407111yescharacteristic
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—942no—
339C4—942no—
340C4—1881no—
341C4—1881no—
342C4—1881no—
343C4—1881no—
344C4—1881no—
345C2—944no—
346C2#126×D4711yescharacteristic
347C2#1568965611yescharacteristic
348C2#1568971411yescharacteristic
349C2#1568979811yescharacteristic
350C2#1568979811yescharacteristic
351C2#1568980911yescharacteristic
352C2#1568980911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#401C2
hypercenter#401D47
hypocenterC47#2493
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. #15689065C2semidirect
2. #15689064C2semidirect
3. #15689064C2semidirect
4. #15689010C2semidirect
5. #15689008C2semidirect
6. #15689006C2semidirect
9. #15688990C2semidirect
15. C47×#401C2semidirect
177. #401D47semidirect
192. C47#2493semidirect