Finite Group Databasebeta

← #20246827

Subgroups — #20246827

Order 6016.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093998C211yesmaximal, characteristic, complemented
2C2×#13093997C211yesmaximal, characteristic, complemented
3C2×#13093996C211yesmaximal, characteristic, complemented
4C2×#13093996C211yesmaximal, characteristic, complemented
5C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
6C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
7#15689047C211yesmaximal, characteristic, complemented
8#15689046C211yesmaximal, characteristic, complemented
9#15689041C211yesmaximal, characteristic, complemented
10#15689038C211yesmaximal, characteristic, complemented
11#15689023C211yesmaximal, characteristic, complemented
12#15689020C211yesmaximal, characteristic, complemented
13#15689000C211yesmaximal, characteristic, complemented
14#15688982C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C23×Dic47C2211yescharacteristic
22C23×Dic47C2211yescharacteristic
23C22×C4×D47C2211yescharacteristic
24#13093998—24no—
25#13093997—24no—
26#13093996—24no—
27#13093996—24no—
28(C22⋊D47)⋊C4—24no—
29C2×C4⋊Dic47C2211yescharacteristic
30C2×Dic47⋊C4—24no—
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×Dic47⋊C4C2211yescharacteristic
35C2×Dic47⋊C4C2211yescharacteristic
36C2×Dic47⋊C4C2211yescharacteristic
37C2×Dic47⋊C4C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×C22⋊Dic47C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C2×(C2×D47)⋊C4C2211yescharacteristic
45C2×(C2×D47)⋊C4C2211yescharacteristic
46C2×(C2×D47)⋊C4C2211yescharacteristic
47C2×C4×Dic47C2211yescharacteristic
48C47⋊#95C2211yescharacteristic
49C47⋊#95C2211yescharacteristic
50C22×D4×C47C2211yescharacteristic
51C23×C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55#95×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×C47—22no—
65C22×C4×C47—22no—
66C22×C4×C47—41no—
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
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—22no—
80C2×C22⋊D47—22no—
81C2×C22⋊D47—22no—
82C2×C22⋊D47—41no—
83C2×C22⋊D47D414yescomplemented
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—22no—
87C22×Dic47—22no—
88C22×Dic47—41no—
89C22×Dic47D414yescomplemented
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C22×Dic47C2311yescharacteristic
93C22×Dic47C2311yescharacteristic
94C22×Dic47C2311yescharacteristic
95C22×Dic47C2311yescharacteristic
96C2×D188—22no—
97C2×D188—22no—
98C2×D188—41no—
99C2×C4×D47—22no—
100C2×C4×D47—22no—
101C2×C4×D47—22no—
102C22⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—41no—
105C22⋊Dic47—22no—
106C22⋊Dic47—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—41no—
114C4⋊Dic47—22no—
115Dic47⋊C4—22no—
116Dic47⋊C4—22no—
117Dic47⋊C4—22no—
118Dic47⋊C4—22no—
119Dic47⋊C4—22no—
120Dic47⋊C4—22no—
121Dic47⋊C4D414yescomplemented
122C4×Dic47—22no—
123C23×C47—21no—
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×C47C2×D412yes—
135C23×C47C2×D412yes—
136C23×C47#4112yes—
137C23×C47C2411yescharacteristic
138C22×D47—21no—
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—
152D4×C47—44no—
153C2×C4×C47—21no—
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—44no—
168C2×C4×C47C2×D412yes—
169C22⋊D47—28no—
170C22⋊D47—44no—
171C22⋊D47—44no—
172C22⋊D47—44no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—28no—
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—44no—
187C2×Dic47C2×D412yes—
188C2×Dic47C2×D412yes—
189C2×Dic47C2×D412yes—
190C2×Dic47C2×D412yes—
191C2×Dic47C2×D412yes—
192C2×Dic47#4112yes—
193D188—44no—
194C4×D47—44no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47#12114yescomplemented
209C22×C47C22×D411yescharacteristic
210C22×C47C22×D411yescharacteristic
211C22×C47C22×D411yescharacteristic
212C22×C47C2×#4111yescharacteristic
213C22×C47C2×#4111yescharacteristic
214C22×C47H(5,𝔽2)11yescharacteristic
215C22×C472−1+411yescharacteristic
216C2×D47—22no—
217C2×D47—22no—
218C2×D47—22no—
219C2×D47—41no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—41no—
223C2×D47—41no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C2×D47—41no—
229C2×D47—41no—
230C4×C47—22no—
231C4×C47—41no—
232C4×C47—41no—
233C4×C47—41no—
234C4×C47—41no—
235Dic47—22no—
236Dic47—22no—
237Dic47—22no—
238Dic47—41no—
239Dic47—41no—
240Dic47#12114yescomplemented
241#2416—471nomaximal, Sylow
242C2×C47—24no—
243C2×C47—81no—
244C2×C47C2×#12111yescharacteristic
245C2×C47C2×#12111yescharacteristic
246C2×C47#53711yescharacteristic
247C2×C47D4211yescharacteristic
248C2×C47#54711yescharacteristic
249C2×C47#54811yescharacteristic
250C2×C47#55311yescharacteristic
251D47—42no—
252D47—81no—
253C2×#121—471no—
254C2×#121—471no—
255C2×#121—471no—
256C2×#121—471no—
257C2×C4×D4—471no—
258C22×C4⋊C4—471no—
259#396—471no—
260#396—471no—
261#394—471no—
262#394—471no—
263#390—471no—
264#389—471no—
265#386—471no—
266#386D4711yescharacteristic, complemented
267#380—471no—
268C47#241611yescharacteristic, complemented, Sylow
269C22×D4—471no—
270C22×D4—471no—
271C22×D4—471no—
272C22×D4—471no—
273C22×D4—471no—
274C22×D4C2×D4711yescharacteristic
275C23×C4—471no—
276C23×C4—471no—
277C23×C4—471no—
278C23×C4C2×D4711yescharacteristic
279#121—944no—
280#121—944no—
281#121—944no—
282#121—944no—
283C4×D4—944no—
284C2×C4⋊C4—471no—
285C2×C4⋊C4—471no—
286C2×C4⋊C4—471no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4—471no—
289C2×C4⋊C4—471no—
290C2×C4⋊C4—471no—
291C2×C4⋊C4—471no—
292C2×C4⋊C4—944no—
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⋊C4—471no—
302C2×C22⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic
305C2×C42—471no—
306#95—471no—
307#95—471no—
308#95C2×D4711yescharacteristic
309#95C2×D4711yescharacteristic
310C24—471no—
311C24—471no—
312C24C22×D4711yescharacteristic
313C24C22×D4711yescharacteristic
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—474no—
318C2×D4—942no—
319C2×D4—942no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—942no—
323C2×D4—942no—
324C2×D4—942no—
325C2×D4—942no—
326C2×D4—942no—
327C2×D4—942no—
328C2×D4—942no—
329C2×D4—942no—
330C2×D4—1881no—
331C2×D4—1881no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—471no—
336C22×C4—474no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—942no—
343C22×C4—942no—
344C22×C4—942no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—1881no—
350C22×C4C22×D4711yescharacteristic
351C22×C4C22×D4711yescharacteristic
352C22×C4C22×D4711yescharacteristic
353C22×C4C22×D4711yescharacteristic
354C22×C4C22×D4711yescharacteristic
355C4⋊C4—474no—
356C4⋊C4—942no—
357C4⋊C4—942no—
358C4⋊C4—942no—
359C4⋊C4—942no—
360C4⋊C4—942no—
361C4⋊C4—942no—
362C4⋊C4—942no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—942no—
367C22⋊C4—942no—
368C22⋊C4—942no—
369C22⋊C4—942no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—1881no—
375C42—942no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—472no—
388C23—941no—
389C23—941no—
390C23—941no—
391C23—941no—
392C23—941no—
393C23—941no—
394C23—941no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23—941no—
401C23#1062535012yes—
402C23D4×D4712yes—
403C23D4×D4712yes—
404C23C23×D4711yescharacteristic
405D4—44no—
406D4—948no—
407D4—1884no—
408D4—1884no—
409D4—1884no—
410D4—1884no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
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—44no—
426C2×C4—472no—
427C2×C4—472no—
428C2×C4—472no—
429C2×C4—472no—
430C2×C4—472no—
431C2×C4—472no—
432C2×C4—948no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—1884no—
446C2×C4—1884no—
447C2×C4D4×D4712yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—942no—
462C22—942no—
463C22—942no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22—1881no—
473C22—1881no—
474C22—1881no—
475C22#1309399714yescomplemented
476C22C2×D4×D4711yescharacteristic
477C22C2×D4×D4711yescharacteristic
478C22C2×D4×D4711yescharacteristic
479C22#41×D4711yescharacteristic
480C22C2×#1062535011yescharacteristic
481C22#1309406911yescharacteristic
482C22#1309407111yescharacteristic
483C4—22no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—474no—
489C4—942no—
490C4—942no—
491C4—942no—
492C4—1881no—
493C4—1881no—
494C2—24no—
495C2—81no—
496C2—3761no—
497C2—1882no—
498C2#121×D4711yescharacteristic
499C2C2×#1309399711yescharacteristic
500C2#1568970011yescharacteristic
501C2#1568975511yescharacteristic
502C2#1568977111yescharacteristic
503C2#1568978211yescharacteristic
504C2#1568982211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2416
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13093998C2semidirect
2. C2×#13093997C2semidirect
3. C2×#13093996C2semidirect
4. C2×#13093996C2semidirect
5. C2×(C22⋊D47)⋊C4C2semidirect
6. C22×Dic47⋊C4C2semidirect
7. #15689047C2semidirect
8. #15689046C2semidirect
9. #15689041C2semidirect
10. #15689038C2semidirect
11. #15689023C2semidirect
12. #15689020C2semidirect
13. #15689000C2semidirect
14. #15688982C2semidirect
15. C47×#386C2semidirect
83. C2×C22⋊D47D4semidirect
89. C22×Dic47D4semidirect
121. Dic47⋊C4D4semidirect
208. C22×C47#121semidirect
240. Dic47#121semidirect
266. #386D47semidirect
268. C47#2416semidirect
475. C22#13093997semidirect