Finite Group Databasebeta

← #26143342

Subgroups — #26143342

Order 12032.

1346 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689043C211yesmaximal, characteristic
2C2×#15689029C211yesmaximal, characteristic
3#20241658C211yesmaximal, characteristic
4#20241652C211yesmaximal, characteristic
5#20241643C212yesmaximal
6#20241641C211yesmaximal, characteristic
7#20241638C212yesmaximal
8Dic47⋊#95C212yesmaximal
9#20241614C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C2×C47×#387C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×Dic47⋊C4C2212yes—
15C22×Dic47⋊C4C2212yes—
16C22×C4×Dic47C2212yes—
17#15689043C418yescomplemented
18#15689029—24no—
19C2×C47⋊#95C2212yes—
20C2×C47⋊#95C2212yes—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2211yescharacteristic
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C22×C4⋊C4×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C47×#387—24no—
34C2×#95×C47C2211yescharacteristic
35C2×#95×C47C2211yescharacteristic
36C2×#95×C47C2211yescharacteristic
37C2×#95×C47C2211yescharacteristic
38C22×Dic94—22no—
39C22×Dic94—22no—
40C22×Dic94—42no—
41C22×Dic94—42no—
42C22×Dic94C2×C414yes—
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C23×Dic47C2312yes—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47—42no—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4—42no—
51C2×Dic47⋊C4—42no—
52C2×Dic47⋊C4—42no—
53C2×Dic47⋊C4—42no—
54C2×Dic47⋊C4C2×C418yes—
55C2×C4×Dic47—42no—
56C2×C4×Dic47—42no—
57C2×C4×Dic47Q818yescomplemented
58C47⋊#95—24no—
59C47⋊#95—24no—
60C47⋊#95—22no—
61C47⋊#95—24no—
62C47⋊#95—24no—
63C47⋊#95—42no—
64C47⋊#95—42no—
65C47⋊#95—42no—
66C47⋊#95—42no—
67C47⋊#95C2×C418yes—
68C47⋊#95C2×C414yes—
69C23×C4×C47C2311yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C23×C4×C47C2311yescharacteristic
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C2×C4⋊C4×C47—22no—
77C2×C4⋊C4×C47—22no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—42no—
80C2×C4⋊C4×C47C2×C414yes—
81C2×C42×C47—42no—
82C2×C42×C47D414yes—
83#95×C47—22no—
84#95×C47—22no—
85#95×C47—22no—
86#95×C47—22no—
87C24×C47C2411yescharacteristic
88C22×C4×C47—22no—
89C22×C4×C47—22no—
90C22×C4×C47—21no—
91C22×C4×C47—22no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—21no—
101C22×C4×C47—22no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47C22×C412yes—
118C22×C4×C47C22×C412yes—
119C22×C4×C47C22×C412yes—
120C22×C4×C47C2×D412yes—
121C22×C4×C47C2×D412yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×Q814yes—
124C22×C4×C47#4112yes—
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47C22×C414yes—
149C22×Dic47C22×C414yes—
150C22×Dic47C2×Q814yes—
151C22×Dic47C2×Q814yes—
152C22×Dic47#4114yes—
153C2×Dic94—28no—
154C2×Dic94—48no—
155C2×Dic94—44no—
156C2×Dic94—44no—
157C2×Dic94—48no—
158C4⋊C4×C47—28no—
159C4⋊C4×C47—44no—
160C42×C47—44no—
161C4⋊Dic47—44no—
162Dic47⋊C4—48no—
163Dic47⋊C4—48no—
164C4×Dic47—48no—
165C23×C47C23×C411yescharacteristic
166C23×C47C22×D411yescharacteristic
167C23×C47C22×Q812yes—
168C23×C47C2×#4112yes—
169C23×C47C2×#4111yescharacteristic
170C23×C47H(5,𝔽2)12yes—
171C23×C47H(5,𝔽2)12yes—
172C23×C47H(5,𝔽2)11yescharacteristic
173C23×C472−1+411yescharacteristic
174C23×C472−1+411yescharacteristic
175C23×C472−1+411yescharacteristic
176C2×C4×C47—24no—
177C2×C4×C47—22no—
178C2×C4×C47—22no—
179C2×C4×C47—22no—
180C2×C4×C47—22no—
181C2×C4×C47—24no—
182C2×C4×C47—24no—
183C2×C4×C47—24no—
184C2×C4×C47—22no—
185C2×C4×C47—22no—
186C2×C4×C47—24no—
187C2×C4×C47—22no—
188C2×C4×C47—22no—
189C2×C4×C47—22no—
190C2×C4×C47—22no—
191C2×C4×C47—22no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47—41no—
195C2×C4×C47—41no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—41no—
199C2×C4×C47—42no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47C4×D414yes—
212C2×C4×C47C4⋊Q814yes—
213C2×Dic47—24no—
214C2×Dic47—24no—
215C2×Dic47—24no—
216C2×Dic47—24no—
217C2×Dic47—24no—
218C2×Dic47—24no—
219C2×Dic47—24no—
220C2×Dic47—24no—
221C2×Dic47—24no—
222C2×Dic47—24no—
223C2×Dic47—24no—
224C2×Dic47—24no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—42no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47—42no—
231C2×Dic47—42no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47C4×Q818yes—
241Dic94—416no—
242#14327—471nomaximal, Sylow
243C22×C47C2×C4×D411yescharacteristic
244C22×C47C2×C4×Q812yes—
245C22×C47#51812yes—
246C22×C47#51911yescharacteristic
247C22×C47#52011yescharacteristic
248C22×C47C2×C4⋊Q811yescharacteristic
249C22×C47#53211yescharacteristic
250C22×C47#53312yes—
251C22×C47#53411yescharacteristic
252C22×C47#53511yescharacteristic
253C22×C47#53611yescharacteristic
254C22×C47#53711yescharacteristic
255C22×C47#53812yes—
256C22×C47#53812yes—
257C22×C47#53912yes—
258C22×C47#54111yescharacteristic
259C22×C47#54212yes—
260C22×C47#54212yes—
261C22×C47#54211yescharacteristic
262C22×C47#54312yes—
263C22×C47#54412yes—
264C22×C47#54412yes—
265C22×C47#54412yes—
266C4×C47—24no—
267C4×C47—24no—
268C4×C47—42no—
269C4×C47—42no—
270C4×C47—42no—
271C4×C47—81no—
272C4×C47—81no—
273Dic47—28no—
274Dic47—44no—
275Dic47—44no—
276Dic47—82no—
277C2×#395—471no—
278C2×#391—471no—
279C2×#387D4711yescharacteristic
280#1446—471no—
281#1444—471no—
282#1442—472no—
283#1441—472no—
284#1441—471no—
285C4⋊#95—472no—
286#1434—472no—
287C4×#95—471no—
288C2×C47C4×C4⋊Q811yescharacteristic
289C2×C47#232111yescharacteristic
290C2×C47#232311yescharacteristic
291C2×C47#232912yes—
292C2×C47#233112yes—
293C2×C47#265911yescharacteristic
294C2×C47#266011yescharacteristic
295C2×C47#266211yescharacteristic
296C2×C47#266311yescharacteristic
297C2×C47#266512yes—
298C2×C47#266612yes—
299C23×Q8—471no—
300C22×C4⋊C4—472no—
301C22×C4⋊C4—472no—
302C22×C4⋊C4—471no—
303C22×C4⋊C4C2×D4711yescharacteristic
304C22×C4⋊C4C2×D4711yescharacteristic
305C22×C42—472no—
306C22×C42C2×D4711yescharacteristic
307#395—478no—
308#391—944no—
309#387—24no—
310C2×#95—471no—
311C2×#95—472no—
312C2×#95—472no—
313C2×#95—471no—
314C2×#95—472no—
315C2×#95—472no—
316C2×#95—472no—
317C2×#95—472no—
318C2×#95—472no—
319C2×#95—472no—
320C2×#95—472no—
321C2×#95C2×D4711yescharacteristic
322C2×#95C2×D4711yescharacteristic
323C2×#95C2×D4711yescharacteristic
324C2×#95C2×D4711yescharacteristic
325C47#1432711yescharacteristic, complemented, Sylow
326C22×Q8—474no—
327C22×Q8—942no—
328C22×Q8—942no—
329C22×Q8—1882no—
330C22×Q8—1882no—
331C23×C4—472no—
332C23×C4—472no—
333C23×C4—472no—
334C23×C4—472no—
335C23×C4C22×D4711yescharacteristic
336C23×C4C22×D4711yescharacteristic
337C23×C4C22×D4711yescharacteristic
338C23×C4C22×D4711yescharacteristic
339C23×C4C22×D4711yescharacteristic
340C23×C4C22×D4711yescharacteristic
341C23×C4C22×D4711yescharacteristic
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—478no—
347C2×C4⋊C4—944no—
348C2×C4⋊C4—942no—
349C2×C4⋊C4—1882no—
350C2×C4⋊C4—1882no—
351C2×C4⋊C4—1882no—
352C2×C4⋊C4—1882no—
353C2×C4⋊C4—1882no—
354C2×C4⋊C4C4×D4714yes—
355C2×C42—42no—
356C2×C42—478no—
357C2×C42—1882no—
358C2×C42—1882no—
359C2×C42C22⋊D4714yes—
360#95—22no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—474no—
365#95—478no—
366#95—944no—
367#95—944no—
368#95—942no—
369#95—944no—
370#95—944no—
371#95—1882no—
372#95—1882no—
373#95—1882no—
374#95—1882no—
375C24C23×D4711yescharacteristic
376C2×Q8—948no—
377C2×Q8—1888no—
378C2×Q8—1884no—
379C2×Q8—1884no—
380C2×Q8—1888no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—474no—
411C22×C4—474no—
412C22×C4—474no—
413C22×C4—474no—
414C22×C4—474no—
415C22×C4—942no—
416C22×C4—942no—
417C22×C4—942no—
418C22×C4—942no—
419C22×C4—942no—
420C22×C4—942no—
421C22×C4—942no—
422C22×C4—942no—
423C22×C4—942no—
424C22×C4—942no—
425C22×C4—942no—
426C22×C4—942no—
427C22×C4—942no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4C2×C4×D4712yes—
439C22×C4C2×C4×D4712yes—
440C22×C4C2×C4×D4712yes—
441C22×C4#1062535012yes—
442C22×C4Q8×D4714yes—
443C22×C4C2×C22⋊D4712yes—
444C22×C4C2×C22⋊D4712yes—
445C22×C4C2×C22⋊D4712yes—
446C4⋊C4—28no—
447C4⋊C4—44no—
448C4⋊C4—1888no—
449C4⋊C4—1884no—
450C4⋊C4—1888no—
451C42—44no—
452C42—1888no—
453C23C22×C4×D4711yescharacteristic
454C23C22×C22⋊D4711yescharacteristic
455C23C2×Q8×D4712yes—
456C23#41×D4712yes—
457C23C2×#1062535011yescharacteristic
458C23#1309406912yes—
459C23#1309407012yes—
460C23#1309407011yescharacteristic
461C23#1309407111yescharacteristic
462C23#1309407111yescharacteristic
463C23#1309407111yescharacteristic
464Q8—18816no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—478no—
501C2×C4—944no—
502C2×C4—944no—
503C2×C4—944no—
504C2×C4—944no—
505C2×C4—944no—
506C2×C4—944no—
507C2×C4—944no—
508C2×C4—944no—
509C2×C4—944no—
510C2×C4—944no—
511C2×C4—944no—
512C2×C4—944no—
513C2×C4—1882no—
514C2×C4—1882no—
515C2×C4—1882no—
516C2×C4—1882no—
517C2×C4—1882no—
518C2×C4—1882no—
519C2×C4—1882no—
520C2×C4—1882no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1882no—
525C2×C4—1882no—
526C2×C4—1882no—
527C2×C4—1882no—
528C2×C4C4×C22⋊D4714yes—
529C2×C4#1309402214yes—
530C22C2×C4×C22⋊D4711yescharacteristic
531C22C4×Q8×D4712yes—
532C22#1568959512yes—
533C22#1568960011yescharacteristic
534C22#1568960311yescharacteristic
535C22C2×#1309402211yescharacteristic
536C22#1568966911yescharacteristic
537C22#1568967712yes—
538C22#1568968211yescharacteristic
539C22#1568968711yescharacteristic
540C22#1568969411yescharacteristic
541C22#1568970111yescharacteristic
542C22#1568970612yes—
543C22#1568971212yes—
544C22#1568971612yes—
545C22#1568973511yescharacteristic
546C22#1568973912yes—
547C22#1568974112yes—
548C22#1568974411yescharacteristic
549C22#1568974812yes—
550C22#1568975212yes—
551C22#1568975312yes—
552C22#1568975312yes—
553C4—24no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—42no—
558C4—81no—
559C4—81no—
560C4—948no—
561C4—3762no—
562C4—1884no—
563C4—1884no—
564C2C4×#1309402211yescharacteristic
565C2#2024604211yescharacteristic
566C2#2024607011yescharacteristic
567C2#2024611512yes—
568C2#2024613312yes—
569C2#2024950411yescharacteristic
570C2#2024950911yescharacteristic
571C2#2024952811yescharacteristic
572C2#2024953811yescharacteristic
573C2#2024956412yes—
574C2#2024957512yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#387C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#387D47
hypocenterC47#14327
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
17. #15689043C4semidirect
57. C2×C4×Dic47Q8semidirect
325. C47#14327semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156890432
C2×#156890292
#202416582
#202416522
#202416432
#202416412
#202416382
Dic47⋊#952
#202416142
C4×C47⋊#952
C2×C47×#3872
#1432747