Finite Group Databasebeta

← #20247014

Subgroups — #20247014

Order 6016.

836 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625350C211yesmaximal, characteristic
2C2×#13094023C211yesmaximal, characteristic, complemented
3C2×#13094010C211yesmaximal, characteristic, complemented
4C2×#13094002C211yesmaximal, characteristic, complemented
5#15689041C211yesmaximal, characteristic, complemented
6#15689040C211yesmaximal, characteristic, complemented
7#15689039C211yesmaximal, characteristic, complemented
8#15689038C211yesmaximal, characteristic, complemented
9#15689027C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15688997C211yesmaximal, characteristic, complemented
12#15688996C211yesmaximal, characteristic, complemented
13#15688994C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#385C211yesmaximal, characteristic, complemented
16C2×#10625350—24no—
17C2×#10625350—24no—
18C2×#10625350—24no—
19C22×Dic94C2211yescharacteristic
20C22×Dic94C2211yescharacteristic
21C22×D188C2211yescharacteristic
22C22×C22⋊D47C2211yescharacteristic
23C22×C22⋊D47C2211yescharacteristic
24C22×C4×D47C2211yescharacteristic
25C22×C4×D47C2211yescharacteristic
26#13094023—24no—
27#13094010—24no—
28#13094002—24no—
29C2×C4⋊Dic47C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C2×C4×Dic47C2211yescharacteristic
45C2×C4×Dic47C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C47⋊#95C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52C2×C4⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55#95×C47C2211yescharacteristic
56#95×C47C2211yescharacteristic
57C24×C47C2311yescharacteristic
58C23×D47C2311yescharacteristic
59C23×D47C2311yescharacteristic
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C2×C22⋊D47—22no—
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47D414yes—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81#10625350—232no—
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—22no—
85C2×C4×D47—22no—
86C2×C4×D47—22no—
87C2×C4×D47—22no—
88C2×C4×D47—22no—
89C2×C4×D47—22no—
90C2×C4×D47D414yes—
91C2×Dic94—22no—
92C2×Dic94—22no—
93C2×Dic94—22no—
94C2×Dic94—22no—
95C2×Dic94—22no—
96C2×Dic94D414yes—
97C4⋊C4×C47—22no—
98C4⋊C4×C47—22no—
99C22⋊C4×C47—22no—
100C22⋊C4×C47—22no—
101C22⋊Dic47—22no—
102C22⋊Dic47—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111C4⋊Dic47—22no—
112Dic47⋊C4—22no—
113Dic47⋊C4—22no—
114Dic47⋊C4—22no—
115Dic47⋊C4—22no—
116C4×Dic47—22no—
117C4×Dic47—22no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47C2×D412yes—
125C23×C47C2411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47C2×D412yes—
139C22×D47C2×D412yes—
140C2×C4×C47—28no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47C2×D412yes—
157C2×C4×C47C2×D412yes—
158C2×C4×C47#4112yescomplemented
159C22⋊D47—28no—
160C22⋊D47—28no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47C2×D412yes—
175C2×Dic47C2×D412yes—
176C2×Dic47C2×D412yes—
177C2×Dic47C2×D412yes—
178C2×Dic47#4112yescomplemented
179D188—28no—
180C4×D47—28no—
181C4×D47—28no—
182Dic94—28no—
183Dic94—44no—
184C22×C47—22no—
185C22×C47—22no—
186C22×C47—22no—
187C22×C47—41no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47C22×D411yescharacteristic
192C22×C47C22×D411yescharacteristic
193C22×C47C22×D411yescharacteristic
194C22×C47C2×#4111yescharacteristic
195C22×C47C2×#4111yescharacteristic
196C22×C472−1+411yescharacteristic
197C22×C472−1+411yescharacteristic
198C2×D47—22no—
199C2×D47—22no—
200C2×D47—22no—
201C2×D47—22no—
202C2×D47—22no—
203C2×D47—22no—
204C2×D47—41no—
205C2×D47—41no—
206C2×D47—41no—
207C2×D47—41no—
208C2×D47—41no—
209C2×D47—41no—
210C2×D47—41no—
211C2×D47—41no—
212C4×C47—22no—
213C4×C47—22no—
214C4×C47—22no—
215C4×C47—41no—
216C4×C47—41no—
217C4×C47—41no—
218Dic47—22no—
219Dic47—22no—
220Dic47—41no—
221Dic47—41no—
222Dic47—41no—
223Dic47#12014yes—
224#2432—471nomaximal, Sylow
225C2×C47—42no—
226C2×C47C2×#12011yescharacteristic
227C2×C47#53211yescharacteristic
228C2×C47#53611yescharacteristic
229C2×C47#54711yescharacteristic
230C2×C47#54711yescharacteristic
231C2×C47#54811yescharacteristic
232C2×C47#54811yescharacteristic
233D47—42no—
234D47—42no—
235C22×#41—471no—
236C2×C4⋊Q8—471no—
237C2×#124—471no—
238C2×C22⋊Q8—471no—
239#394—471no—
240#394—471no—
241#394—471no—
242#394—471no—
243#391—471no—
244#390—471no—
245#385—471no—
246#385—471no—
247#385—471no—
248#385D4711yescharacteristic, complemented
249C4×C22⋊C4—471no—
250C47#243211yescharacteristic, complemented, Sylow
251C2×#41—944no—
252C2×#41—944no—
253C2×#41—944no—
254C22×Q8—471no—
255C22×Q8—471no—
256C22×D4—471no—
257C22×D4—471no—
258C22×D4—471no—
259C23×C4—471no—
260C23×C4—471no—
261C23×C4C2×D4711yescharacteristic
262C4⋊Q8—944no—
263#124—944no—
264C22⋊Q8—944no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4—471no—
267C2×C4⋊C4—471no—
268C2×C4⋊C4—471no—
269C2×C4⋊C4—471no—
270C2×C4⋊C4C2×D4711yescharacteristic
271C2×C4⋊C4C2×D4711yescharacteristic
272C2×C22⋊C4—471no—
273C2×C22⋊C4—471no—
274C2×C22⋊C4—471no—
275C2×C22⋊C4—471no—
276C2×C22⋊C4—471no—
277C2×C22⋊C4—471no—
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—471no—
282C2×C22⋊C4C2×D4711yescharacteristic
283C2×C22⋊C4C2×D4711yescharacteristic
284C2×C42—471no—
285C2×C42—471no—
286#95—471no—
287#95—471no—
288#95—471no—
289#95—471no—
290#95C2×D4711yescharacteristic
291#95C2×D4711yescharacteristic
292C24—471no—
293C24—471no—
294C24C22×D4711yescharacteristic
295#41—9432no—
296C2×Q8—474no—
297C2×Q8—942no—
298C2×Q8—942no—
299C2×Q8—942no—
300C2×Q8—942no—
301C2×Q8—942no—
302C2×D4—474no—
303C2×D4—942no—
304C2×D4—942no—
305C2×D4—942no—
306C2×D4—942no—
307C2×D4—942no—
308C2×D4—942no—
309C2×D4—942no—
310C2×D4—942no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—471no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—474no—
318C22×C4—471no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4—942no—
322C22×C4—942no—
323C22×C4—942no—
324C22×C4—942no—
325C22×C4—942no—
326C22×C4C22×D4711yescharacteristic
327C22×C4C22×D4711yescharacteristic
328C22×C4C22×D4711yescharacteristic
329C22×C4C22×D4711yescharacteristic
330C22×C4C22×D4711yescharacteristic
331C22×C4C22×D4711yescharacteristic
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—942no—
335C4⋊C4—942no—
336C4⋊C4—942no—
337C4⋊C4—942no—
338C4⋊C4—942no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—942no—
342C22⋊C4—942no—
343C22⋊C4—942no—
344C22⋊C4—942no—
345C22⋊C4—942no—
346C22⋊C4—942no—
347C22⋊C4—942no—
348C22⋊C4—942no—
349C22⋊C4—942no—
350C22⋊C4—942no—
351C42—942no—
352C42—942no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—472no—
360C23—472no—
361C23—941no—
362C23—941no—
363C23—941no—
364C23—941no—
365C23—941no—
366C23—941no—
367C23—941no—
368C23—941no—
369C23—941no—
370C23—941no—
371C23—941no—
372C23—941no—
373C23D4×D4712yes—
374C23C23×D4711yescharacteristic
375Q8—948no—
376Q8—1884no—
377D4—948no—
378D4—948no—
379D4—948no—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—472no—
397C2×C4—472no—
398C2×C4—472no—
399C2×C4—472no—
400C2×C4—472no—
401C2×C4—948no—
402C2×C4—948no—
403C2×C4—941no—
404C2×C4—941no—
405C2×C4—941no—
406C2×C4—941no—
407C2×C4—941no—
408C2×C4—941no—
409C2×C4—941no—
410C2×C4—941no—
411C2×C4—941no—
412C2×C4—941no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4#1062535012yescomplemented
417C2×C4D4×D4712yes—
418C2×C4D4×D4712yes—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—942no—
427C22—942no—
428C22—942no—
429C22—942no—
430C22—942no—
431C22—942no—
432C22—1881no—
433C22—1881no—
434C22—1881no—
435C22—1881no—
436C22—1881no—
437C22—1881no—
438C22—1881no—
439C22—1881no—
440C22C2×D4×D4711yescharacteristic
441C22C2×D4×D4711yescharacteristic
442C22C2×D4×D4711yescharacteristic
443C22#41×D4711yescharacteristic
444C22C2×#1062535011yescharacteristic
445C22#1309407111yescharacteristic
446C22#1309407211yescharacteristic
447C4—22no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—41no—
452C4—41no—
453C4—474no—
454C4—942no—
455C4—942no—
456C4—1881no—
457C4—1881no—
458C4—1881no—
459C2—42no—
460C2—1882no—
461C2—1882no—
462C2#120×D4711yescharacteristic
463C2#1568967011yescharacteristic
464C2#1568969611yescharacteristic
465C2#1568977111yescharacteristic
466C2#1568977411yescharacteristic
467C2#1568978211yescharacteristic
468C2#1568978311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2432
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#13094023C2semidirect
3. C2×#13094010C2semidirect
4. C2×#13094002C2semidirect
5. #15689041C2semidirect
6. #15689040C2semidirect
7. #15689039C2semidirect
8. #15689038C2semidirect
9. #15689027C2semidirect
10. #15689023C2semidirect
11. #15688997C2semidirect
12. #15688996C2semidirect
13. #15688994C2semidirect
14. #15688970C2semidirect
15. C47×#385C2semidirect
158. C2×C4×C47#41semidirect
178. C2×Dic47#41semidirect
248. #385D47semidirect
250. C47#2432semidirect
416. C2×C4#10625350semidirect