Finite Group Databasebeta

← #20246728

Subgroups — #20246728

Order 6016.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625352C211yesmaximal, characteristic, complemented
2C2×#13094002C211yesmaximal, characteristic, complemented
3C2×#13093997C211yesmaximal, characteristic, complemented
4C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
5#15689038C211yesmaximal, characteristic, complemented
6#15689032C211yesmaximal, characteristic, complemented
7#15689031C211yesmaximal, characteristic, complemented
8#15689027C211yesmaximal, characteristic, complemented
9#15689023C211yesmaximal, characteristic, complemented
10#15689001C211yesmaximal, characteristic, complemented
11#15689000C211yesmaximal, characteristic, complemented
12#15688995C211yesmaximal, characteristic, complemented
13#15688994C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C47×#394C211yesmaximal, characteristic, complemented
16C2×#10625352—24no—
17C2×#10625352—24no—
18C2×#10625352—24no—
19C22×Dic94C2211yescharacteristic
20C22×D188C2211yescharacteristic
21C22×C22⋊D47C2211yescharacteristic
22C22×C22⋊D47C2211yescharacteristic
23C22×C22⋊D47C2211yescharacteristic
24C22×C22⋊D47C2211yescharacteristic
25C23×Dic47C2211yescharacteristic
26C23×Dic47C2211yescharacteristic
27C22×C4×D47C2211yescharacteristic
28C22×C4×D47C2211yescharacteristic
29#13094002—24no—
30#13093997—24no—
31(C22⋊D47)⋊C4—24no—
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×Dic47⋊C4C2211yescharacteristic
35C2×Dic47⋊C4C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×C22⋊Dic47C2211yescharacteristic
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
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C47⋊#95C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C2×C22⋊C4×C47C2211yescharacteristic
56#95×C47C2211yescharacteristic
57C24×C47C2311yescharacteristic
58C24×C47C2311yescharacteristic
59C23×D47C2311yescharacteristic
60C23×D47C2311yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—22no—
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⋊D47—22no—
75C2×C22⋊D47—22no—
76C2×C22⋊D47—22no—
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—41no—
80C2×C22⋊D47D414yescomplemented
81C22×Dic47—22no—
82C22×Dic47—22no—
83C22×Dic47—22no—
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47D414yescomplemented
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C22×Dic47C2311yescharacteristic
93#10625352—232no—
94C2×D188—22no—
95C2×D188—22no—
96C2×D188—41no—
97C2×C4×D47—22no—
98C2×C4×D47—22no—
99C2×C4×D47—22no—
100C2×C4×D47—22no—
101C2×C4×D47—22no—
102C2×C4×D47—22no—
103C2×Dic94—22no—
104C2×Dic94—22no—
105C2×Dic94D414yescomplemented
106C4⋊C4×C47—22no—
107C22⋊C4×C47—22no—
108C22⋊C4×C47—22no—
109C22⋊C4×C47—41no—
110C22⋊C4×C47—41no—
111C22⋊Dic47—22no—
112C22⋊Dic47—41no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115(C2×D47)⋊C4—22no—
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—22no—
118(C2×D47)⋊C4—41no—
119Dic47⋊C4—22no—
120Dic47⋊C4—22no—
121Dic47⋊C4—22no—
122Dic47⋊C4—22no—
123C4×Dic47—22no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47C2×D412yes—
137C23×C47C2×D412yes—
138C23×C47C2411yescharacteristic
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47—21no—
148C22×D47—21no—
149C22×D47—21no—
150C22×D47—21no—
151C22×D47C2×D412yes—
152C22×D47#4112yescomplemented
153D4×C47—28no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47C2×D412yes—
169C22⋊D47—28no—
170C22⋊D47—28no—
171C22⋊D47—28no—
172C22⋊D47—44no—
173C2×Dic47—28no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—28no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47C2×D412yes—
188C2×Dic47C2×D412yes—
189C2×Dic47C2×D412yes—
190C2×Dic47C2×D412yes—
191C2×Dic47C2×D412yes—
192C2×Dic47#4112yescomplemented
193D188—44no—
194C4×D47—28no—
195C4×D47—44no—
196Dic94—28no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—22no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—41no—
210C22×C47—41no—
211C22×C47C22×D411yescharacteristic
212C22×C47C22×D411yescharacteristic
213C22×C47C22×D411yescharacteristic
214C22×C47C2×#4111yescharacteristic
215C22×C47C2×#4111yescharacteristic
216C22×C47H(5,𝔽2)11yescharacteristic
217C22×C472−1+411yescharacteristic
218C2×D47—22no—
219C2×D47—22no—
220C2×D47—22no—
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C2×D47—41no—
229C2×D47—41no—
230C2×D47—41no—
231C2×D47—41no—
232C4×C47—22no—
233C4×C47—41no—
234C4×C47—41no—
235C4×C47—41no—
236C4×C47—41no—
237Dic47—22no—
238Dic47—22no—
239Dic47—22no—
240Dic47—41no—
241Dic47—41no—
242Dic47#12014yes—
243#2407—471nomaximal, Sylow
244C2×C47—42no—
245C2×C47—42no—
246C2×C47C2×#12011yescharacteristic
247C2×C47#52511yescharacteristic
248C2×C47#53711yescharacteristic
249C2×C47#54611yescharacteristic
250C2×C47#54711yescharacteristic
251C2×C47#54811yescharacteristic
252C2×C47#55011yescharacteristic
253D47—42no—
254D47—42no—
255C22×#41—471no—
256C2×C22⋊Q8—471no—
257C2×#121—471no—
258C2×C4×D4—471no—
259#394—471no—
260#394D4711yescharacteristic, complemented
261#392—471no—
262#392—471no—
263#391—471no—
264#390—471no—
265#386—471no—
266#386—471no—
267#385—471no—
268#385—471no—
269#380—471no—
270C47#240711yescharacteristic, complemented, Sylow
271C2×#41—944no—
272C2×#41—944no—
273C2×#41—944no—
274C22×Q8—471no—
275C22×D4—471no—
276C22×D4—471no—
277C22×D4—471no—
278C22×D4—471no—
279C22×D4—471no—
280C22×D4C2×D4711yescharacteristic
281C23×C4—471no—
282C23×C4—471no—
283C23×C4—471no—
284C23×C4—471no—
285C22⋊Q8—944no—
286#121—944no—
287C4×D4—944no—
288C2×C4⋊C4—471no—
289C2×C4⋊C4—471no—
290C2×C4⋊C4—471no—
291C2×C4⋊C4—471no—
292C2×C4⋊C4C2×D4711yescharacteristic
293C2×C22⋊C4—471no—
294C2×C22⋊C4—471no—
295C2×C22⋊C4—471no—
296C2×C22⋊C4—471no—
297C2×C22⋊C4—471no—
298C2×C22⋊C4—471no—
299C2×C22⋊C4—471no—
300C2×C22⋊C4—471no—
301C2×C22⋊C4C2×D4711yescharacteristic
302C2×C22⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic
305C2×C42—471no—
306#95—471no—
307#95—471no—
308#95—471no—
309#95—471no—
310#95—471no—
311#95C2×D4711yescharacteristic
312C24—471no—
313C24—471no—
314C24C22×D4711yescharacteristic
315C24C22×D4711yescharacteristic
316#41—9432no—
317C2×Q8—474no—
318C2×Q8—942no—
319C2×Q8—942no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—474no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—942no—
328C2×D4—942no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—942no—
332C2×D4—942no—
333C2×D4—942no—
334C2×D4—942no—
335C2×D4—942no—
336C2×D4—1881no—
337C2×D4—1881no—
338C22×C4—471no—
339C22×C4—474no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—471no—
343C22×C4—471no—
344C22×C4—471no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—942no—
350C22×C4—942no—
351C22×C4—942no—
352C22×C4—942no—
353C22×C4—942no—
354C22×C4—942no—
355C22×C4—942no—
356C22×C4C22×D4711yescharacteristic
357C22×C4C22×D4711yescharacteristic
358C22×C4C22×D4711yescharacteristic
359C22×C4C22×D4711yescharacteristic
360C22×C4C22×D4711yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—942no—
363C4⋊C4—942no—
364C4⋊C4—942no—
365C4⋊C4—942no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—942no—
375C22⋊C4—942no—
376C22⋊C4—1881no—
377C22⋊C4—1881no—
378C42—942no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—472no—
392C23—472no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23—941no—
401C23—941no—
402C23—941no—
403C23—941no—
404C23—941no—
405C23D4×D4712yes—
406C23D4×D4712yes—
407C23C23×D4711yescharacteristic
408Q8—948no—
409D4—28no—
410D4—948no—
411D4—948no—
412D4—948no—
413D4—1884no—
414D4—1884no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—472no—
430C2×C4—472no—
431C2×C4—472no—
432C2×C4—472no—
433C2×C4—472no—
434C2×C4—472no—
435C2×C4—948no—
436C2×C4—948no—
437C2×C4—948no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—941no—
446C2×C4—941no—
447C2×C4—941no—
448C2×C4—941no—
449C2×C4—941no—
450C2×C4—1884no—
451C2×C4D4×D4712yes—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—942no—
467C22—942no—
468C22—942no—
469C22—942no—
470C22—942no—
471C22—942no—
472C22—1881no—
473C22—1881no—
474C22—1881no—
475C22—1881no—
476C22—1881no—
477C22—1881no—
478C22—1881no—
479C22—1881no—
480C22C2×D4×D4711yescharacteristic
481C22C2×D4×D4711yescharacteristic
482C22C2×D4×D4711yescharacteristic
483C22#41×D4711yescharacteristic
484C22#41×D4711yescharacteristic
485C22#1309406911yescharacteristic
486C22#1309407111yescharacteristic
487C4—22no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—41no—
492C4—474no—
493C4—942no—
494C4—942no—
495C4—942no—
496C4—1881no—
497C4—1881no—
498C2—42no—
499C2—42no—
500C2—1882no—
501C2—1882no—
502C2#120×D4711yescharacteristic
503C2#1568963111yescharacteristic
504C2#1568970011yescharacteristic
505C2#1568976211yescharacteristic
506C2#1568977111yescharacteristic
507C2#1568978111yescharacteristic
508C2#1568979111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#394C2
hypercenter#394D47
hypocenterC47#2407
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#10625352C2semidirect
2. C2×#13094002C2semidirect
3. C2×#13093997C2semidirect
4. C2×(C22⋊D47)⋊C4C2semidirect
5. #15689038C2semidirect
6. #15689032C2semidirect
7. #15689031C2semidirect
8. #15689027C2semidirect
9. #15689023C2semidirect
10. #15689001C2semidirect
11. #15689000C2semidirect
12. #15688995C2semidirect
13. #15688994C2semidirect
14. #15688981C2semidirect
15. C47×#394C2semidirect
80. C2×C22⋊D47D4semidirect
86. C22×Dic47D4semidirect
105. C2×Dic94D4semidirect
152. C22×D47#41semidirect
192. C2×Dic47#41semidirect
260. #394D47semidirect
270. C47#2407semidirect