Finite Group Databasebeta

← #20252460

Subgroups — #20252460

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689670C211yesmaximal, characteristic
2#15689199C211yesmaximal, characteristic, complemented
3#15689198C211yesmaximal, characteristic, complemented
4#15689196C211yesmaximal, characteristic, complemented
5#15689195C211yesmaximal, characteristic, complemented
6#15689193C211yesmaximal, characteristic, complemented
7C8×C22⋊D47C211yesmaximal, characteristic, complemented
8(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
9#15689178C211yesmaximal, characteristic, complemented
10#15689175C211yesmaximal, characteristic, complemented
11#15689091C211yesmaximal, characteristic, complemented
12#15689089C211yesmaximal, characteristic, complemented
13#15689088C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#435C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625350C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21C22×C47⋊C8C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic
23C2×C8×D47C2211yescharacteristic
24#13094023C411yescharacteristic
25#13094020C411yescharacteristic
26#13094010C411yescharacteristic
27#13094010C411yescharacteristic
28#13093999C411yescharacteristic
29#13093997C411yescharacteristic
30#13093997C411yescharacteristic
31#13093995C411yescharacteristic
32C4×D188C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35C42×D47C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic
37Dic47⋊C8C2211yescharacteristic
38Dic47⋊C8C2211yescharacteristic
39C22⋊(C47⋊C8)C2211yescharacteristic
40C22⋊(C47⋊C8)C2211yescharacteristic
41(C2×D47)⋊C8C2211yescharacteristic
42(C2×D47)⋊C8C2211yescharacteristic
43(C2×D47)⋊C8C2211yescharacteristic
44(C2×D47)⋊C8C2211yescharacteristic
45(C2×D47)⋊C8C2211yescharacteristic
46(C2×D47)⋊C8C2211yescharacteristic
47(C2×D47)⋊C8C2211yescharacteristic
48(C2×D47)⋊C8C2211yescharacteristic
49#13093935C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C22⋊C8×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×D4×C47C2×C411yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47C2×C411yescharacteristic
63C2×C22⋊D47C2×C411yescharacteristic
64C2×C22⋊D47C2×C411yescharacteristic
65C2×C22⋊D47C2×C411yescharacteristic
66C2×C22⋊D47C2×C411yescharacteristic
67C2×C22⋊D47C2×C411yescharacteristic
68#10625350—41no—
69#10625350—41no—
70#10625350—41no—
71#10625350—41no—
72C2×D188C2×C411yescharacteristic
73C2×D188C2×C411yescharacteristic
74C2×D188C2×C411yescharacteristic
75C2×C4×D47C2×C411yescharacteristic
76C2×C4×D47C2×C411yescharacteristic
77C2×C4×D47C2311yescharacteristic
78C2×C4×D47C2311yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×Dic94C2×C411yescharacteristic
81C2×Dic94C2×C411yescharacteristic
82M16×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C2×C8×C47C2311yescharacteristic
88C4⋊C4×C47C2×C411yescharacteristic
89C22⋊C4×C47C2×C411yescharacteristic
90C22⋊C4×C47C2×C411yescharacteristic
91C42×C47C2311yescharacteristic
92C22⋊Dic47C2×C411yescharacteristic
93C22⋊Dic47C2×C411yescharacteristic
94(C2×D47)⋊C4C2×C411yescharacteristic
95(C2×D47)⋊C4C2×C411yescharacteristic
96(C2×D47)⋊C4C2×C411yescharacteristic
97(C2×D47)⋊C4C2×C411yescharacteristic
98C4⋊Dic47C2×C411yescharacteristic
99Dic47⋊C4C2×C411yescharacteristic
100Dic47⋊C4C2×C411yescharacteristic
101C4×Dic47C2×C411yescharacteristic
102C4×Dic47C2×C411yescharacteristic
103C4×Dic47C2311yescharacteristic
104#10625329—41no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111#10625324—41no—
112C8×D47—41no—
113C8×D47—41no—
114C23×C47C22×C411yescharacteristic
115C23×C47C22×C411yescharacteristic
116C22×D47C22×C411yescharacteristic
117C22×D47C22×C411yescharacteristic
118C22×D47C22×C411yescharacteristic
119D4×C47—41no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47C22×C411yescharacteristic
125C2×C4×C47C22×C411yescharacteristic
126C2×C4×C47C22×C411yescharacteristic
127C2×C4×C47C22×C411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47—22no—
130C22⋊D47—22no—
131C22⋊D47—41no—
132C22⋊D47—41no—
133C22⋊D47—41no—
134C22⋊D47—41no—
135C2×Dic47C22×C411yescharacteristic
136C2×Dic47C22×C411yescharacteristic
137C2×Dic47C22×C411yescharacteristic
138C2×Dic47C22×C411yescharacteristic
139C2×Dic47C22×C411yescharacteristic
140D188—41no—
141D188—41no—
142D188—41no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—22no—
150C4×D47—41no—
151Dic94—41no—
152Dic94—41no—
153C8×C47—21no—
154C8×C47—21no—
155C8×C47—21no—
156C8×C47—21no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47C23×C411yescharacteristic
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—21no—
171C2×D47—21no—
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47H(5,𝔽2)11yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—21no—
186Dic47—21no—
187Dic47#13112yes—
188#2981—471nomaximal, Sylow
189C2×C47—41no—
190C2×C47—41no—
191C2×C47#51811yescharacteristic
192C2×C47C2×#13111yescharacteristic
193C2×C47#56811yescharacteristic
194D47—41no—
195D47—41no—
196D47—41no—
197#532—471no—
198#436—471no—
199#436—471no—
200#435—471no—
201#435—471no—
202#435—471no—
203#435D4711yescharacteristic, complemented
204C8×D4—471no—
205C8×D4—471no—
206#432—471no—
207#431—471no—
208#408—471no—
209#408—471no—
210#408—471no—
211#408—471no—
212C47#298111yescharacteristic, complemented, Sylow
213C2×#41—471no—
214C2×#41—471no—
215C2×M16—471no—
216C2×M16—471no—
217C2×M16—471no—
218C2×M16C2×D4711yescharacteristic
219C22×C8—471no—
220C22×C8—471no—
221C22×C8—471no—
222C22×C8C2×D4711yescharacteristic
223C4⋊Q8—471no—
224#127—471no—
225#124—471no—
226#124—471no—
227#121—471no—
228#121—471no—
229#121—471no—
230#121—471no—
231C4×D4—471no—
232C4×D4—471no—
233C4×D4—471no—
234C4×D4C2×D4711yescharacteristic
235C2×C42—471no—
236C4⋊C8—471no—
237C4⋊C8—471no—
238C4⋊C8—471no—
239C4⋊C8C2×D4711yescharacteristic
240C22⋊C8—471no—
241C22⋊C8—471no—
242C22⋊C8—471no—
243C22⋊C8—471no—
244C22⋊C8—471no—
245C22⋊C8—471no—
246C22⋊C8—471no—
247C22⋊C8—471no—
248C22⋊C8—471no—
249C22⋊C8—471no—
250C22⋊C8C2×D4711yescharacteristic
251C22⋊C8C2×D4711yescharacteristic
252#97—471no—
253#97C2×D4711yescharacteristic
254C4×C8—471no—
255C4×C8—471no—
256#41—1881no—
257#41—1881no—
258#41—1881no—
259#41—1881no—
260C2×Q8—471no—
261C2×Q8—471no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—471no—
268C2×D4—471no—
269C2×D4—471no—
270C2×D4—471no—
271C2×D4C4×D4711yescharacteristic
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4C22×D4711yescharacteristic
278C22×C4C22×D4711yescharacteristic
279M16—41no—
280M16—1881no—
281M16—1881no—
282M16—1881no—
283C2×C8—41no—
284C2×C8—471no—
285C2×C8—471no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—1881no—
289C2×C8—1881no—
290C2×C8—1881no—
291C2×C8C22×D4711yescharacteristic
292C2×C8C22×D4711yescharacteristic
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—471no—
296C4⋊C4—471no—
297C4⋊C4—471no—
298C4⋊C4C4×D4711yescharacteristic
299C22⋊C4—471no—
300C22⋊C4—471no—
301C22⋊C4—471no—
302C22⋊C4—471no—
303C22⋊C4—471no—
304C22⋊C4—471no—
305C22⋊C4C4×D4711yescharacteristic
306C22⋊C4C4×D4711yescharacteristic
307C42—471no—
308C42—471no—
309C42—471no—
310C42C22×D4711yescharacteristic
311C23—471no—
312C23—471no—
313C23—471no—
314C23C2×C4×D4711yescharacteristic
315C23C2×C4×D4711yescharacteristic
316Q8—1881no—
317Q8—1881no—
318D4—41no—
319D4—942no—
320D4—942no—
321D4—1881no—
322D4—1881no—
323D4—1881no—
324D4—1881no—
325D4—1881no—
326D4—1881no—
327D4—1881no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—471no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—942no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—1881no—
345C2×C4C2×C4×D4711yescharacteristic
346C2×C4C2×C4×D4711yescharacteristic
347C2×C4C2×C4×D4711yescharacteristic
348C2×C4C2×C4×D4711yescharacteristic
349C2×C4C23×D4711yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—941no—
355C8—941no—
356C8—941no—
357C8—941no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—941no—
365C22—941no—
366C22—941no—
367C22—941no—
368C22—941no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22C22×C4×D4711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—472no—
379C4—941no—
380C4—941no—
381C4—941no—
382C4—941no—
383C4#1309406911yescharacteristic
384C4#1309407011yescharacteristic
385C2—41no—
386C2—41no—
387C2—1881no—
388C2—1881no—
389C2—1881no—
390C2#1568959511yescharacteristic
391C2#131×D4711yescharacteristic
392C2#1568988911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D47
commutator, socleC22×C47C23×C4
FittingC47×#435C2
hypercenter#435D47
hypocenterC47#2981
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #15689199C2semidirect
3. #15689198C2semidirect
4. #15689196C2semidirect
5. #15689195C2semidirect
6. #15689193C2semidirect
7. C8×C22⋊D47C2semidirect
8. (C22⋊D47)⋊C8C2semidirect
9. #15689178C2semidirect
10. #15689175C2semidirect
11. #15689091C2semidirect
12. #15689089C2semidirect
13. #15689088C2semidirect
14. #15689088C2semidirect
15. C47×#435C2semidirect
203. #435D47semidirect
212. C47#2981semidirect