Finite Group Databasebeta

← #26186178

Subgroups — #26186178

Order 12032.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253406C211yesmaximal, characteristic
2#20252357C211yesmaximal, characteristic, complemented
3#41×C47⋊C8C211yesmaximal, characteristic, complemented
4#20242235C211yesmaximal, characteristic, complemented
5#20242228C211yesmaximal, characteristic, complemented
6#20242221C211yesmaximal, characteristic, complemented
7#20242214C211yesmaximal, characteristic, complemented
8#20242192C211yesmaximal, characteristic, complemented
9#20242191C211yesmaximal, characteristic, complemented
10#20242185C211yesmaximal, characteristic, complemented
11#20242180C211yesmaximal, characteristic, complemented
12#20242169C211yesmaximal, characteristic, complemented
13#20241797C211yesmaximal, characteristic, complemented
14#20241672C211yesmaximal, characteristic, complemented
15C47×#1488C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689464C411yescharacteristic
18#15689447C411yescharacteristic
19#15689430C411yescharacteristic
20#15689423C411yescharacteristic
21#15689345C411yescharacteristic
22#15689338C411yescharacteristic
23#15689285C411yescharacteristic
24#15689268C411yescharacteristic
25#15689250C2211yescharacteristic
26Q8×C47⋊C8C2211yescharacteristic
27Q8×C47⋊C8C2211yescharacteristic
28#15689247C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625334C2211yescharacteristic
33#15689200C2211yescharacteristic
34#15689191—21no—
35D4×C47⋊C8—21no—
36D4×C47⋊C8—21no—
37D4×C47⋊C8C2211yescharacteristic
38D4×C47⋊C8C2211yescharacteristic
39#15689188C2211yescharacteristic
40(C22⋊D47)⋊C8—21no—
41#15689185—21no—
42#15689176—21no—
43#15689176C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689080—21no—
46C2×C4×C47⋊C8—21no—
47C2×C4×C47⋊C8C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C4×#41×C47C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625324—21no—
72C22×C47⋊C8—21no—
73C22×C47⋊C8—21no—
74C22×C47⋊C8D411yescharacteristic
75C22×C47⋊C8D411yescharacteristic
76C2×C8×D47—21no—
77#13094018—21no—
78#13094016C2×C411yescharacteristic
79#13094012C2×C411yescharacteristic
80#13094007—21no—
81#13094003C2×C411yescharacteristic
82#13093998C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×D188C2311yescharacteristic
85C4×C22⋊D47—21no—
86#13093981—21no—
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91C4⋊(C47⋊C8)—21no—
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)C2×C411yescharacteristic
94C4⋊(C47⋊C8)C2×C411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093947C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)C2×C411yescharacteristic
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114#13093934—21no—
115C4×C47⋊C8—21no—
116C4×C47⋊C8—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8D411yescharacteristic
119C4×C47⋊C8D411yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C2×#41×C47C2×C411yescharacteristic
126C4×Q8×C47C2×C411yescharacteristic
127C4×Q8×C47C2311yescharacteristic
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47C2×C411yescharacteristic
131C4×D4×C47C2311yescharacteristic
132#117×C47—21no—
133#117×C47C2×C411yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—22no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×D4×C47—21no—
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C2×C22⋊D47—21no—
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×Dic94C22×C411yescharacteristic
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47C22×C411yescharacteristic
166C4⋊C4×C47C22×C411yescharacteristic
167C22⋊C4×C47—21no—
168C22⋊C4×C47—21no—
169C22⋊C4×C47—21no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47C22×C411yescharacteristic
174C42×C47C2×D411yescharacteristic
175C42×C47#4111yescharacteristic
176C42×C47C2411yescharacteristic
177C22⋊Dic47—21no—
178#10625337—22no—
179#10625336—22no—
180#10625335—22no—
181#10625334—22no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47C22×C411yescharacteristic
187C4⋊Dic47C22×C411yescharacteristic
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192C4×Dic47—21no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—42no—
198C2×C47⋊C8—42no—
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207#10625324—42no—
208C8×D47—42no—
209C23×C47—21no—
210C23×C47C4×D411yescharacteristic
211C22×D47—21no—
212Q8×C47—21no—
213Q8×C47#13112yes—
214D4×C47—24no—
215D4×C47—21no—
216D4×C47#13112yes—
217C2×C4×C47—24no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—42no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C4×D411yescharacteristic
232C2×C4×C47C23×C411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C22⋊D47—42no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239D188—21no—
240D188—21no—
241C4×D47—41no—
242C4×D47—41no—
243Dic94—21no—
244Dic94—21no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257C47⋊C8#13512yes—
258C47⋊C8#13512yes—
259#17904—471nomaximal, Sylow
260C22×C47—21no—
261C22×C47—22no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47C2×C4×D411yescharacteristic
267C2×D47—41no—
268C2×D47—41no—
269C2×D47—41no—
270C4×C47—21no—
271C4×C47—22no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47C2×#13111yescharacteristic
278C4×C47C2×#13111yescharacteristic
279C4×C47C2×#13511yescharacteristic
280C4×C47C2×#13511yescharacteristic
281Dic47—41no—
282Dic47—41no—
283Dic47—41no—
284#3102—471no—
285#2966—471no—
286C8×#41—471no—
287#1584—471no—
288#1583—471no—
289#1582—471no—
290#1581—471no—
291C8×Q16—471no—
292C8×SD16—471no—
293C8×SD16—471no—
294C8×D8—471no—
295#1572—471no—
296#1488D4711yescharacteristic, complemented
297#1482—471no—
298#1450—471no—
299C2×C47—41no—
300C2×C47—42no—
301C2×C47#292911yescharacteristic
302C2×C47C4×#13511yescharacteristic
303C2×C47#295511yescharacteristic
304D47—81no—
305#529—471no—
306C4×#41C2×D4711yescharacteristic
307#485—471no—
308#482—471no—
309#479—471no—
310#478—471no—
311#464—471no—
312#463—471no—
313#452—471no—
314#449—471no—
315#446—471no—
316C8×Q8—471no—
317C8×Q8—471no—
318C8×Q8—471no—
319C4×Q16—471no—
320C4×SD16—471no—
321C4×SD16—471no—
322C4×D8—471no—
323#436—471no—
324#435—941no—
325C8×D4—471no—
326C8×D4—471no—
327C8×D4—471no—
328C8×D4—941no—
329C8×D4—941no—
330C8×D4—941no—
331#433—941no—
332#432C2×D4711yescharacteristic
333#431—471no—
334#431—471no—
335#431—941no—
336#431C2×D4711yescharacteristic
337#405—941no—
338C2×C4×C8—471no—
339C2×C4×C8—941no—
340#335—471no—
341#335—471no—
342#334—471no—
343#334—471no—
344Q8⋊C8—471no—
345Q8⋊C8—471no—
346Q8⋊C8C2×D4711yescharacteristic
347Q8⋊C8C2×D4711yescharacteristic
348D4⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8C2×D4711yescharacteristic
351D4⋊C8C2×D4711yescharacteristic
352#322—471no—
353#322—471no—
354C82—471no—
355C82—471no—
356C47#1790411yescharacteristic, complemented, Sylow
357C2×#41C4×D4711yescharacteristic
358C2×Q16—471no—
359C2×SD16—471no—
360C2×SD16—471no—
361C2×D8—471no—
362C2×M16—941no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—941no—
366C22×C8—941no—
367C22×C8—941no—
368#126—941no—
369#125—471no—
370#124—471no—
371#123—941no—
372C22⋊Q8—471no—
373#121—471no—
374C4×Q8—471no—
375C4×Q8C4×D4711yescharacteristic
376C4×Q8C22×D4711yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—471no—
380C4×D4—941no—
381C4×D4C4×D4711yescharacteristic
382C4×D4C22×D4711yescharacteristic
383#117—21no—
384#117—941no—
385#117C4×D4711yescharacteristic
386C2×C42—21no—
387C2×C42C22×D4711yescharacteristic
388#107—471no—
389#107—471no—
390#106—471no—
391#106—471no—
392C4⋊C8—21no—
393C4⋊C8—471no—
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—941no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8C22×D4711yescharacteristic
402C4⋊C8C22×D4711yescharacteristic
403#103—471no—
404#103—471no—
405#103—471no—
406#103—471no—
407#102—471no—
408#102—471no—
409#102—471no—
410#102—471no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—471no—
414C22⋊C8—471no—
415C22⋊C8—941no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—21no—
421#97—941no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—941no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434#41—22no—
435#41—22no—
436C2×Q8—471no—
437C2×Q8C2×C4×D4711yescharacteristic
438C2×D4—21no—
439C2×D4—471no—
440C2×D4—941no—
441C2×D4C2×C4×D4711yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—941no—
446C22×C4C2×C4×D4711yescharacteristic
447C22×C4D4×D4711yescharacteristic
448C22×C4#1062535211yescharacteristic
449Q16—942no—
450SD16—942no—
451SD16—942no—
452D8—942no—
453M16—1882no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—471no—
459C2×C8—471no—
460C2×C8—471no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—942no—
467C2×C8—942no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—1882no—
471C2×C8—1882no—
472C2×C8—1882no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—471no—
476C4⋊C4—471no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4C2×C4×D4711yescharacteristic
482C4⋊C4C2×C4×D4711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—941no—
487C22⋊C4—941no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—941no—
495C42C2×C4×D4711yescharacteristic
496C42D4×D4711yescharacteristic
497C42#1062535211yescharacteristic
498C42C23×D4711yescharacteristic
499C23—21no—
500C23—941no—
501C23(C22⋊D47)⋊C411yescharacteristic
502Q8—21no—
503Q8—941no—
504Q8—941no—
505Q8#1309403212yes—
506D4—24no—
507D4—21no—
508D4—941no—
509D4—941no—
510D4—1882no—
511D4#1309403212yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4(C22⋊D47)⋊C411yescharacteristic
530C2×C4(C22⋊D47)⋊C411yescharacteristic
531C2×C4(C22⋊D47)⋊C411yescharacteristic
532C2×C4C22×C4×D4711yescharacteristic
533C2×C4C2×D4×D4711yescharacteristic
534C2×C4C2×#1062535211yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—472no—
540C8—472no—
541C8—941no—
542C8—941no—
543C8—941no—
544C8—941no—
545C8—941no—
546C8—941no—
547C8—1881no—
548C8—1881no—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—1881no—
556C22—1881no—
557C22—1881no—
558C22C2×(C22⋊D47)⋊C411yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—22no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—1881no—
567C4—1881no—
568C4—1881no—
569C4C2×#1309403211yescharacteristic
570C4C2×#1309403211yescharacteristic
571C4#135×D4711yescharacteristic
572C4#135×D4711yescharacteristic
573C2—41no—
574C2—42no—
575C2—3761no—
576C2#2025207811yescharacteristic
577C2#2025215611yescharacteristic
578C2#2025228711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1488C2
socleC22×C47C2×C4×D4
prime radical#15689268C4
cosocleC42×C47C24
hypercenter#1488D47
hypocenterC47#17904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #20252357C2semidirect
3. #41×C47⋊C8C2semidirect
4. #20242235C2semidirect
5. #20242228C2semidirect
6. #20242221C2semidirect
7. #20242214C2semidirect
8. #20242192C2semidirect
9. #20242191C2semidirect
10. #20242185C2semidirect
11. #20242180C2semidirect
12. #20242169C2semidirect
13. #20241797C2semidirect
14. #20241672C2semidirect
15. C47×#1488C2semidirect
296. #1488D47semidirect
356. C47#17904semidirect

Maximal subgroups

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

subgroupindex
#202534062
#202523572
#41×C47⋊C82
#202422352
#202422282
#202422212
#202422142
#202421922
#202421912
#202421852
#202421802
#202421692
#202417972
#202416722
C47×#14882
#1790447