Finite Group Databasebeta

← #20250596

Subgroups — #20250596

Order 6016.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689058C211yesmaximal, characteristic, complemented
2#15689058C211yesmaximal, characteristic, complemented
3#15689057C211yesmaximal, characteristic, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689047C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689025C211yesmaximal, characteristic
8#15689007C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic
10#15689001C211yesmaximal, characteristic
11#15688997C211yesmaximal, characteristic, complemented
12#15688997C211yesmaximal, characteristic, complemented
13#15688982C211yesmaximal, characteristic, complemented
14#15688980C211yesmaximal, characteristic, complemented
15C47×#387C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C2×C4⋊C4×C47C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C42×C47C2211yescharacteristic
47#95×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C23×D47C2311yescharacteristic
52C23×D47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C2×D188—41no—
67C2×D188—41no—
68C2×D188Q814yes—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—41no—
72C2×C4×D47—41no—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—41no—
77C42×C47—41no—
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—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91Dic47⋊C4—22no—
92Dic47⋊C4—41no—
93Dic47⋊C4—41no—
94Dic47⋊C4—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97C23×C47C2411yescharacteristic
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—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47C2×Q812yes—
111C22×D47C2×Q812yes—
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—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47C2×Q812yes—
132C2×C4×C47#4112yes—
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—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47#4112yes—
151D188—44no—
152C4×D47—44no—
153C4×D47—44no—
154C22×C47C22×Q811yescharacteristic
155C22×C47C2×#4111yescharacteristic
156C22×C47C2×#4111yescharacteristic
157C22×C47H(5,𝔽2)11yescharacteristic
158C22×C47H(5,𝔽2)11yescharacteristic
159C22×C47H(5,𝔽2)11yescharacteristic
160C22×C47H(5,𝔽2)11yescharacteristic
161C2×D47—22no—
162C2×D47—22no—
163C2×D47—22no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C4×C47—22no—
176C4×C47—22no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182Dic47—22no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187Dic47—41no—
188#2748—471nomaximal, Sylow
189C2×C47#54011yescharacteristic
190C2×C47#54011yescharacteristic
191C2×C47#54311yescharacteristic
192C2×C47#55111yescharacteristic
193C2×C47#55411yescharacteristic
194C2×C47#55411yescharacteristic
195C2×C47#56011yescharacteristic
196D47—42no—
197D47—42no—
198#399—471no—
199#399—471no—
200#398—471no—
201#398—471no—
202#396—471no—
203#396—471no—
204#390—471no—
205#387—471no—
206#387D4711yescharacteristic, complemented
207#386—471no—
208#386—471no—
209#385—471no—
210#385—471no—
211#380—471no—
212#380—471no—
213C47#274811yescharacteristic, complemented, Sylow
214C22×D4—471no—
215C23×C4—471no—
216C23×C4—471no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4C2×D4711yescharacteristic
227C2×C4⋊C4C2×D4711yescharacteristic
228C2×C22⋊C4—471no—
229C2×C22⋊C4—471no—
230C2×C22⋊C4—471no—
231C2×C22⋊C4—471no—
232C2×C22⋊C4—471no—
233C2×C22⋊C4—471no—
234C2×C22⋊C4—471no—
235C2×C22⋊C4—471no—
236C2×C22⋊C4—471no—
237C2×C22⋊C4—471no—
238C2×C42C2×D4711yescharacteristic
239#95—471no—
240#95—471no—
241#95—471no—
242#95—471no—
243#95—471no—
244#95—471no—
245#95C2×D4711yescharacteristic
246#95C2×D4711yescharacteristic
247#95C2×D4711yescharacteristic
248#95C2×D4711yescharacteristic
249C24—471no—
250C24—471no—
251C2×D4—474no—
252C2×D4—1881no—
253C2×D4—1881no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—942no—
261C22×C4—942no—
262C22×C4—1881no—
263C22×C4—1881no—
264C22×C4—1881no—
265C22×C4—1881no—
266C22×C4C22×D4711yescharacteristic
267C22×C4C22×D4711yescharacteristic
268C22×C4C22×D4711yescharacteristic
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—942no—
276C4⋊C4—1881no—
277C4⋊C4—1881no—
278C4⋊C4—1881no—
279C4⋊C4—1881no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C4⋊C4—1881no—
283C4⋊C4—1881no—
284C22⋊C4—942no—
285C22⋊C4—942no—
286C22⋊C4—1881no—
287C22⋊C4—1881no—
288C22⋊C4—1881no—
289C22⋊C4—1881no—
290C22⋊C4—1881no—
291C22⋊C4—1881no—
292C22⋊C4—1881no—
293C22⋊C4—1881no—
294C42—41no—
295C23—472no—
296C23—472no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23—941no—
302C23—941no—
303C23—941no—
304C23—941no—
305C23—941no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23C23×D4711yescharacteristic
310D4—1884no—
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—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—472no—
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—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—1884no—
349C2×C4—1884no—
350C2×C4#1062535012yes—
351C2×C4Q8×D4712yes—
352C22—942no—
353C22—942no—
354C22—942no—
355C22—942no—
356C22—942no—
357C22—942no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22C2×Q8×D4711yescharacteristic
367C22#41×D4711yescharacteristic
368C22C2×#1062535011yescharacteristic
369C22#1309406911yescharacteristic
370C22#1309407011yescharacteristic
371C22#1309407011yescharacteristic
372C22#1309407011yescharacteristic
373C4—22no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—942no—
381C4—1881no—
382C4—1881no—
383C4—1881no—
384C4—1881no—
385C4—1881no—
386C2—1882no—
387C2—1882no—
388C2#1568972411yescharacteristic
389C2#1568972511yescharacteristic
390C2#1568974811yescharacteristic
391C2#1568979711yescharacteristic
392C2#1568982911yescharacteristic
393C2#1568983311yescharacteristic
394C2#1568986411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2748
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #15689058C2semidirect
2. #15689058C2semidirect
3. #15689057C2semidirect
4. #15689055C2semidirect
5. #15689047C2semidirect
6. #15689045C2semidirect
8. #15689007C2semidirect
11. #15688997C2semidirect
12. #15688997C2semidirect
13. #15688982C2semidirect
14. #15688980C2semidirect
15. C47×#387C2semidirect
206. #387D47semidirect
213. C47#2748semidirect