Finite Group Databasebeta

← #20246016

Subgroups — #20246016

Order 6016.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2#15689015C211yesmaximal, characteristic, complemented
3#15689013C211yesmaximal, characteristic, complemented
4#15689010C211yesmaximal, characteristic, complemented
5#15689004C211yesmaximal, characteristic, complemented
6#15689002C211yesmaximal, characteristic
7#15689000C211yesmaximal, characteristic
8#15688998C211yesmaximal, characteristic, complemented
9#15688990C211yesmaximal, characteristic, complemented
10#15688988C211yesmaximal, characteristic, complemented
11#15688985C211yesmaximal, characteristic, complemented
12#15688980C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C47⋊#95C211yesmaximal, characteristic, complemented
15C47×#385C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20(C22⋊D47)⋊C4C418yescomplemented
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C23×C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52C24×C47C2311yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—41no—
56C22×C4×C47—41no—
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—22no—
64C2×C22⋊D47—22no—
65C2×C22⋊D47C2×C414yes—
66C22×Dic47—22no—
67C22×Dic47—41no—
68C22×Dic47—41no—
69C22×Dic47—41no—
70C22×Dic47—41no—
71C22×Dic47C2×C414yes—
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C2×C4×D47—41no—
80C2×C4×D47—41no—
81C2×C4×D47C2×C414yescomplemented
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C22⋊C4×C47—22no—
85C22⋊C4×C47C2×C414yes—
86C22⋊Dic47—22no—
87(C2×D47)⋊C4—41no—
88(C2×D47)⋊C4—41no—
89(C2×D47)⋊C4—41no—
90(C2×D47)⋊C4—41no—
91(C2×D47)⋊C4C2×C414yescomplemented
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94Dic47⋊C4C2×C414yescomplemented
95C4×Dic47—41no—
96C4×Dic47—41no—
97C4×Dic47C2×C414yescomplemented
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47C22×C412yes—
103C23×C47#4112yes—
104C23×C47#4112yes—
105C23×C47C2411yescharacteristic
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47C22×C412yes—
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—44no—
130C2×C4×C47C22×C412yes—
131C2×C4×C47C22×C412yes—
132C22⋊D47—28no—
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—21no—
151C2×Dic47—44no—
152C2×Dic47—44no—
153C2×Dic47C22×C412yes—
154C2×Dic47C22×C412yes—
155C2×Dic47C22×C412yes—
156C4×D47—44no—
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47#11714yes—
164C22×C47C23×C411yescharacteristic
165C22×C47C2×#4111yescharacteristic
166C22×C47C2×#4111yescharacteristic
167C22×C47H(5,𝔽2)11yescharacteristic
168C22×C47H(5,𝔽2)11yescharacteristic
169C22×C47H(5,𝔽2)11yescharacteristic
170C22×C472−1+411yescharacteristic
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—22no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C4×C47—22no—
179C4×C47—22no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184Dic47—22no—
185Dic47—22no—
186Dic47—22no—
187Dic47—41no—
188Dic47—41no—
189Dic47—41no—
190Dic47—41no—
191#2318—471nomaximal, Sylow
192C2×C47—24no—
193C2×C47C2×#11711yescharacteristic
194C2×C47#51811yescharacteristic
195C2×C47#52011yescharacteristic
196C2×C47#53811yescharacteristic
197C2×C47#53811yescharacteristic
198C2×C47#53911yescharacteristic
199C2×C47#53911yescharacteristic
200D47—42no—
201C2×C4×D4—471no—
202#388—471no—
203#388—471no—
204#387—471no—
205#387—471no—
206#386—471no—
207#386—471no—
208#385—471no—
209#385D4711yescharacteristic, complemented
210#383—471no—
211#382—471no—
212#381—471no—
213#380—471no—
214C4×C22⋊C4—471no—
215C2×#95—471no—
216C47#231811yescharacteristic, complemented, Sylow
217C22×D4—471no—
218C23×C4—471no—
219C23×C4—471no—
220C23×C4—471no—
221C23×C4C2×D4711yescharacteristic
222C4×D4—478no—
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⋊C4C2×D4711yescharacteristic
235C2×C22⋊C4C2×D4711yescharacteristic
236C2×C42—471no—
237C2×C42—471no—
238C2×C42—471no—
239#95—471no—
240#95—471no—
241#95—471no—
242#95—471no—
243#95—471no—
244#95—471no—
245#95—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249#95—471no—
250#95—471no—
251#95C2×D4711yescharacteristic
252#95C2×D4711yescharacteristic
253C24—471no—
254C24C22×D4711yescharacteristic
255C2×D4—474no—
256C2×D4—942no—
257C2×D4—942no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—474no—
265C22×C4—474no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—942no—
271C22×C4—1881no—
272C22×C4—1881no—
273C22×C4—1881no—
274C22×C4—1881no—
275C22×C4—1881no—
276C22×C4—1881no—
277C22×C4C22×D4711yescharacteristic
278C22×C4C22×D4711yescharacteristic
279C22×C4C22×D4711yescharacteristic
280C22×C4C22×D4711yescharacteristic
281C22×C4C22×D4711yescharacteristic
282C22×C4C22×D4711yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—474no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C22⋊C4—22no—
289C22⋊C4—474no—
290C22⋊C4—942no—
291C22⋊C4—1881no—
292C22⋊C4—1881no—
293C22⋊C4—1881no—
294C22⋊C4—1881no—
295C22⋊C4C4×D4714yes—
296C42—474no—
297C42—1881no—
298C42—1881no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—472no—
304C23—941no—
305C23—941no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23C2×C4×D4712yes—
311C23#1062535212yes—
312C23#1062535412yes—
313C23C23×D4711yescharacteristic
314D4—948no—
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—21no—
331C2×C4—44no—
332C2×C4—472no—
333C2×C4—472no—
334C2×C4—472no—
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—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—1884no—
354C2×C4—1884no—
355C2×C4—1884no—
356C2×C4C2×C4×D4712yes—
357C2×C4C2×C4×D4712yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—942no—
365C22—942no—
366C22—942no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22#1309398214yes—
372C22C22×C4×D4711yescharacteristic
373C22C2×#1062535211yescharacteristic
374C22C2×#1062535411yescharacteristic
375C22#1309406911yescharacteristic
376C22#1309406911yescharacteristic
377C22#1309407011yescharacteristic
378C22#1309407111yescharacteristic
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—942no—
386C4—942no—
387C4—942no—
388C4—1881no—
389C4—1881no—
390C4—1881no—
391C4—1881no—
392C2—24no—
393C2—1882no—
394C2C2×#1309398211yescharacteristic
395C2#1568959511yescharacteristic
396C2#1568960211yescharacteristic
397C2#1568970811yescharacteristic
398C2#1568971311yescharacteristic
399C2#1568971711yescharacteristic
400C2#1568972211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#385C2
socleC23×C47C24
hypercenter#385D47
hypocenterC47#2318
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #15689015C2semidirect
3. #15689013C2semidirect
4. #15689010C2semidirect
5. #15689004C2semidirect
8. #15688998C2semidirect
9. #15688990C2semidirect
10. #15688988C2semidirect
11. #15688985C2semidirect
12. #15688980C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C2×C47⋊#95C2semidirect
15. C47×#385C2semidirect
20. (C22⋊D47)⋊C4C4semidirect
81. C2×C4×D47C2×C4semidirect
91. (C2×D47)⋊C4C2×C4semidirect
94. Dic47⋊C4C2×C4semidirect
97. C4×Dic47C2×C4semidirect
209. #385D47semidirect
216. C47#2318semidirect