Finite Group Databasebeta

← #20250642

Subgroups — #20250642

Order 6016.

442 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689063C211yesmaximal, characteristic, complemented
2#15689052C211yesmaximal, characteristic, complemented
3#15689052C211yesmaximal, characteristic, complemented
4#15689041C211yesmaximal, characteristic
5#15689034C211yesmaximal, characteristic, complemented
6#15689034C211yesmaximal, characteristic, complemented
7#15689025C211yesmaximal, characteristic
8#15689013C211yesmaximal, characteristic, complemented
9#15689012C211yesmaximal, characteristic, complemented
10#15689008C211yesmaximal, characteristic, complemented
11#15689007C211yesmaximal, characteristic, complemented
12#15689001C211yesmaximal, characteristic
13#15688994C211yesmaximal, characteristic, complemented
14#15688985C211yesmaximal, characteristic, complemented
15C47×#391C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊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
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C22×Q8×C47C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C42×C47C2211yescharacteristic
47#95×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C23×D47C2311yescharacteristic
52C23×D47C2311yescharacteristic
53C2×Q8×C47—22no—
54C2×Q8×C47—41no—
55C2×Q8×C47—41no—
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C2×D188—22no—
70C2×D188—22no—
71C2×D188—41no—
72C2×C4×D47—22no—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75C4⋊C4×C47—41no—
76C42×C47—41no—
77(C2×D47)⋊C4—22no—
78(C2×D47)⋊C4—22no—
79(C2×D47)⋊C4—22no—
80(C2×D47)⋊C4—41no—
81(C2×D47)⋊C4—41no—
82(C2×D47)⋊C4—41no—
83(C2×D47)⋊C4—41no—
84(C2×D47)⋊C4—41no—
85(C2×D47)⋊C4—41no—
86(C2×D47)⋊C4—41no—
87(C2×D47)⋊C4—41no—
88C4⋊Dic47—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—41no—
91Dic47⋊C4—41no—
92C4×Dic47—41no—
93C23×C47C2411yescharacteristic
94C22×D47—21no—
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47#4112yes—
108Q8×C47—44no—
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×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47#4112yes—
129C2×C4×C47#4112yes—
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×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148D188—44no—
149C4×D47—44no—
150C22×C47C2×#4111yescharacteristic
151C22×C47C2×#4111yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47H(5,𝔽2)11yescharacteristic
154C22×C47H(5,𝔽2)11yescharacteristic
155C22×C47H(5,𝔽2)11yescharacteristic
156C22×C472−1+411yescharacteristic
157C2×D47—22no—
158C2×D47—22no—
159C2×D47—22no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47—41no—
178Dic47—41no—
179Dic47—41no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183Dic47—41no—
184#2751—471nomaximal, Sylow
185C2×C47#53811yescharacteristic
186C2×C47#53811yescharacteristic
187C2×C47#54211yescharacteristic
188C2×C47#55111yescharacteristic
189C2×C47#55211yescharacteristic
190C2×C47#55911yescharacteristic
191C2×C47#56211yescharacteristic
192D47—42no—
193D47—81no—
194#400—471no—
195#397—471no—
196#397—471no—
197#394—471no—
198#393—471no—
199#393—471no—
200#391D4711yescharacteristic, complemented
201#390—471no—
202#388—471no—
203#388—471no—
204#387—471no—
205#387—471no—
206#386—471no—
207#385—471no—
208#381—471no—
209C47#275111yescharacteristic, complemented, Sylow
210C22×Q8C2×D4711yescharacteristic
211C22×D4—471no—
212C23×C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4C2×D4711yescharacteristic
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C22⋊C4—471no—
221C2×C22⋊C4—471no—
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C22⋊C4—471no—
226C2×C22⋊C4—471no—
227C2×C22⋊C4—471no—
228C2×C22⋊C4—471no—
229C2×C42—471no—
230C2×C42C2×D4711yescharacteristic
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95—471no—
238#95—471no—
239#95—471no—
240#95—471no—
241#95C2×D4711yescharacteristic
242#95C2×D4711yescharacteristic
243#95C2×D4711yescharacteristic
244#95C2×D4711yescharacteristic
245C24—471no—
246C24—471no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—942no—
251C2×D4—942no—
252C2×D4—1881no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—942no—
260C22×C4—1881no—
261C22×C4—1881no—
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264C22×C4C22×D4711yescharacteristic
265C22×C4C22×D4711yescharacteristic
266C22×C4C22×D4711yescharacteristic
267C22×C4C22×D4711yescharacteristic
268C22×C4C22×D4711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—942no—
271C4⋊C4—942no—
272C4⋊C4—1881no—
273C4⋊C4—1881no—
274C22⋊C4—942no—
275C22⋊C4—942no—
276C22⋊C4—942no—
277C22⋊C4—1881no—
278C22⋊C4—1881no—
279C22⋊C4—1881no—
280C22⋊C4—1881no—
281C22⋊C4—1881no—
282C22⋊C4—1881no—
283C22⋊C4—1881no—
284C22⋊C4—1881no—
285C42—41no—
286C42—1881no—
287C23—472no—
288C23—941no—
289C23—941no—
290C23—941no—
291C23—941no—
292C23—941no—
293C23—941no—
294C23—941no—
295C23—941no—
296C23—941no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23C23×D4711yescharacteristic
302Q8—44no—
303D4—1884no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—1884no—
342C2×C4#1062535012yes—
343C2×C4#1062535412yes—
344C22—942no—
345C22—942no—
346C22—942no—
347C22—1881no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22#41×D4711yescharacteristic
359C22C2×#1062535011yescharacteristic
360C22C2×#1062535411yescharacteristic
361C22#1309406911yescharacteristic
362C22#1309406911yescharacteristic
363C22#1309407011yescharacteristic
364C22#1309407211yescharacteristic
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—1881no—
373C4—1881no—
374C4—1881no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C2—3761no—
379C2—1882no—
380C2#1568970711yescharacteristic
381C2#1568971111yescharacteristic
382C2#1568974711yescharacteristic
383C2#1568980011yescharacteristic
384C2#1568981411yescharacteristic
385C2#1568985811yescharacteristic
386C2#1568986911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2751
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #15689063C2semidirect
2. #15689052C2semidirect
3. #15689052C2semidirect
5. #15689034C2semidirect
6. #15689034C2semidirect
8. #15689013C2semidirect
9. #15689012C2semidirect
10. #15689008C2semidirect
11. #15689007C2semidirect
13. #15688994C2semidirect
14. #15688985C2semidirect
15. C47×#391C2semidirect
200. #391D47semidirect
209. C47#2751semidirect