Finite Group Databasebeta

← #20248586

Subgroups — #20248586

Order 6016.

548 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094014C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D47C211yesmaximal, characteristic
3#15689047C211yesmaximal, characteristic, complemented
4#15689046C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689023C211yesmaximal, characteristic
8#15689023C211yesmaximal, characteristic
9#15688997C211yesmaximal, characteristic, complemented
10#15688996C211yesmaximal, characteristic, complemented
11#15688994C211yesmaximal, characteristic, complemented
12#15688992C211yesmaximal, characteristic, complemented
13#15688987C211yesmaximal, characteristic, complemented
14#15688974C211yesmaximal, characteristic, complemented
15C47×#385C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18#13094014—24no—
19C4×C22⋊D47—24no—
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×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C23×C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C23×D47C2311yescharacteristic
55C22×C4×C47—22no—
56C22×C4×C47—41no—
57C22×C4×C47—41no—
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—22no—
65C2×C22⋊D47—22no—
66C2×C22⋊D47Q814yes—
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C2×C4×D47—22no—
75C2×C4×D47—41no—
76C2×C4×D47—41no—
77C4⋊C4×C47—22no—
78C4⋊C4×C47—41no—
79C22⋊C4×C47—22no—
80C22⋊C4×C47—41no—
81C22⋊Dic47—22no—
82C22⋊Dic47—22no—
83C22⋊Dic47—41no—
84(C2×D47)⋊C4—22no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—41no—
88(C2×D47)⋊C4—41no—
89C4⋊Dic47—22no—
90C4⋊Dic47—41no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—22no—
94Dic47⋊C4—22no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—41no—
99Dic47⋊C4—41no—
100C4×Dic47—22no—
101C4×Dic47—22no—
102C4×Dic47D414yes—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47C2×Q812yes—
110C23×C47C2411yescharacteristic
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47C2×Q812yes—
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×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—44no—
135C2×C4×C47C2×D412yes—
136C2×C4×C47#4112yes—
137C22⋊D47—28no—
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—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47C2×D412yes—
155C2×Dic47C2×D412yes—
156C2×Dic47C2×Q812yes—
157C2×Dic47#4112yes—
158C2×Dic47#4112yes—
159C4×D47—44no—
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47C22×D411yescharacteristic
168C22×C47C22×Q811yescharacteristic
169C22×C47C2×#4111yescharacteristic
170C22×C47C2×#4111yescharacteristic
171C22×C47C2×#4111yescharacteristic
172C22×C47H(5,𝔽2)11yescharacteristic
173C22×C47H(5,𝔽2)11yescharacteristic
174C2×D47—22no—
175C2×D47—22no—
176C2×D47—22no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C4×C47—22no—
182C4×C47—22no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47—41no—
187Dic47—22no—
188Dic47—22no—
189Dic47—41no—
190Dic47—41no—
191Dic47—41no—
192Dic47—41no—
193Dic47C22⋊Q814yes—
194#2566—471nomaximal, Sylow
195C2×C47—42no—
196C2×C47C2×C22⋊Q811yescharacteristic
197C2×C47#53211yescharacteristic
198C2×C47#53511yescharacteristic
199C2×C47#55311yescharacteristic
200C2×C47#55311yescharacteristic
201C2×C47#55411yescharacteristic
202C2×C47#55411yescharacteristic
203D47—42no—
204C2×#125—471no—
205C2×C4×D4—471no—
206#396—471no—
207#396—471no—
208#396—471no—
209#396—471no—
210#390—471no—
211#390—471no—
212#385—471no—
213#385—471no—
214#385—471no—
215#385D4711yescharacteristic, complemented
216#384—471no—
217#382—471no—
218C4×C4⋊C4—471no—
219C47#256611yescharacteristic, complemented, Sylow
220C22×D4—471no—
221C23×C4—471no—
222C23×C4C2×D4711yescharacteristic
223#125—944no—
224C4×D4—944no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4—471no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4C2×D4711yescharacteristic
237C2×C4⋊C4C2×D4711yescharacteristic
238C2×C22⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4C2×D4711yescharacteristic
247C2×C22⋊C4C2×D4711yescharacteristic
248C2×C42—471no—
249C2×C42—471no—
250C2×C42—471no—
251#95—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95C2×D4711yescharacteristic
256#95C2×D4711yescharacteristic
257C24—471no—
258C24C22×D4711yescharacteristic
259C2×D4—474no—
260C2×D4—942no—
261C2×D4—942no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—471no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—942no—
273C22×C4—1881no—
274C22×C4—1881no—
275C22×C4C22×D4711yescharacteristic
276C22×C4C22×D4711yescharacteristic
277C22×C4C22×D4711yescharacteristic
278C22×C4C22×D4711yescharacteristic
279C22×C4C22×D4711yescharacteristic
280C22×C4C22×D4711yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—942no—
284C4⋊C4—942no—
285C4⋊C4—942no—
286C4⋊C4—942no—
287C4⋊C4—942no—
288C4⋊C4—942no—
289C4⋊C4—942no—
290C4⋊C4—942no—
291C4⋊C4—1881no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—942no—
297C22⋊C4—942no—
298C22⋊C4—942no—
299C22⋊C4—942no—
300C22⋊C4—942no—
301C22⋊C4—1881no—
302C22⋊C4—1881no—
303C22⋊C4—1881no—
304C42—474no—
305C42—942no—
306C42—942no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—472no—
314C23—941no—
315C23—941no—
316C23—941no—
317C23—941no—
318C23—941no—
319C23—941no—
320C23Q8×D4712yes—
321C23C23×D4711yescharacteristic
322D4—948no—
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—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4—472no—
341C2×C4—472no—
342C2×C4—472no—
343C2×C4—472no—
344C2×C4—472no—
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—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—1884no—
362C2×C4#1062535012yes—
363C2×C4D4×D4712yes—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—942no—
372C22—942no—
373C22—942no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22C2×D4×D4711yescharacteristic
379C22C2×Q8×D4711yescharacteristic
380C22#41×D4711yescharacteristic
381C22#41×D4711yescharacteristic
382C22C2×#1062535011yescharacteristic
383C22#1309406911yescharacteristic
384C22#1309406911yescharacteristic
385C4—22no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—474no—
392C4—942no—
393C4—942no—
394C4—1881no—
395C4—1881no—
396C4—1881no—
397C4—1881no—
398C2—42no—
399C2—1882no—
400C2C22⋊Q8×D4711yescharacteristic
401C2#1568967011yescharacteristic
402C2#1568968811yescharacteristic
403C2#1568981811yescharacteristic
404C2#1568982211yescharacteristic
405C2#1568982711yescharacteristic
406C2#1568982811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2566
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13094014C2semidirect
3. #15689047C2semidirect
4. #15689046C2semidirect
5. #15689046C2semidirect
6. #15689045C2semidirect
9. #15688997C2semidirect
10. #15688996C2semidirect
11. #15688994C2semidirect
12. #15688992C2semidirect
13. #15688987C2semidirect
14. #15688974C2semidirect
15. C47×#385C2semidirect
215. #385D47semidirect
219. C47#2566semidirect