Finite Group Databasebeta

← #26182442

Subgroups — #26182442

Order 12032.

1012 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689724C211yesmaximal, characteristic
2#20252417C211yesmaximal, characteristic, complemented
3#20241749C212yesmaximal, complemented
4#20241747C212yesmaximal, complemented
5#20241737C212yesmaximal, complemented
6#20241734C212yesmaximal, complemented
7#20241728C212yesmaximal, complemented
8#20241720C212yesmaximal, complemented
9C47×#2973C211yesmaximal, characteristic, complemented
10#15689724—24no—
11#15689724—24no—
12C2×#13094020C411yescharacteristic
13C2×#13094015C411yescharacteristic
14C2×#13094007C2211yescharacteristic
15C2×#13094007C2211yescharacteristic
16C2×#13094006C411yescharacteristic
17C2×#13094006C411yescharacteristic
18C2×#13093999C411yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×#13093998C2211yescharacteristic
21C2×#13093997C411yescharacteristic
22C2×#13093997C411yescharacteristic
23C2×#13093995C411yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×#13093981C2211yescharacteristic
26#15689195—24no—
27#15689180C2212yes—
28#15689087C2212yes—
29C2×C22⋊(C47⋊C8)C2212yes—
30#15688848C2214yes—
31#15688846C2214yes—
32#15688846C2214yes—
33#15688846C2214yes—
34C2×C4×D4×C47C2211yescharacteristic
35C47×#435—24no—
36C47×#432C2212yes—
37C47×#407C2212yes—
38C2×C22⋊C8×C47C2212yes—
39C22×D188C2×C411yescharacteristic
40C22×D188C2×C411yescharacteristic
41C22×D188C2×C411yescharacteristic
42C22×C22⋊D47C2×C411yescharacteristic
43C22×C22⋊D47C2×C411yescharacteristic
44C22×C22⋊D47C2×C411yescharacteristic
45C22×C22⋊D47C2×C411yescharacteristic
46C22×C22⋊D47C2×C411yescharacteristic
47C22×C22⋊D47C2×C411yescharacteristic
48C22×C4×D47C2×C411yescharacteristic
49C22×C4×D47C2×C411yescharacteristic
50C22×C4×D47C2×C411yescharacteristic
51C2×#10625329—22no—
52C22×C47⋊C8—22no—
53#13094020—24no—
54#13094015—24no—
55#13094007—22no—
56#13094007—22no—
57#13094007—22no—
58#13094007—22no—
59#13094006—24no—
60#13094006—24no—
61#13093999—24no—
62#13093998—22no—
63#13093998—22no—
64#13093998—22no—
65#13093998—22no—
66#13093997—24no—
67#13093997—24no—
68#13093995—24no—
69C4×D188—22no—
70C4×D188—22no—
71#13093981—22no—
72#13093981—22no—
73C2×C4⋊Dic47C2×C411yescharacteristic
74C2×C4⋊Dic47C2×C411yescharacteristic
75C2×C4⋊Dic47C2×C411yescharacteristic
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2311yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×(C2×D47)⋊C4C2×C411yescharacteristic
85C2×(C2×D47)⋊C4C2311yescharacteristic
86C2×(C2×D47)⋊C4C2311yescharacteristic
87C2×(C2×D47)⋊C4C2311yescharacteristic
88C2×C4×Dic47C2×C411yescharacteristic
89C4⋊(C47⋊C8)—22no—
90C22⋊(C47⋊C8)—22no—
91C22⋊(C47⋊C8)—22no—
92C22⋊(C47⋊C8)C2314yes—
93#13093935—22no—
94C22×D4×C47C2×C411yescharacteristic
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C2×M16×C47—22no—
98C22×C8×C47—22no—
99C4×D4×C47D414yes—
100C4×D4×C47D414yes—
101C2×C4⋊C4×C47C2×C411yescharacteristic
102C2×C22⋊C4×C47C2×C411yescharacteristic
103C2×C22⋊C4×C47C2×C411yescharacteristic
104C2×C42×C47C2311yescharacteristic
105C4⋊C8×C47—22no—
106C22⋊C8×C47—22no—
107C22⋊C8×C47—22no—
108C22⋊C8×C47C2314yes—
109#97×C47—22no—
110C24×C47C22×C411yescharacteristic
111C24×C47C22×C411yescharacteristic
112C23×D47C22×C411yescharacteristic
113C23×D47C22×C411yescharacteristic
114C23×D47C22×C411yescharacteristic
115C2×D4×C47—42no—
116C2×D4×C47C22⋊C414yes—
117C22×C4×C47—81no—
118C22×C4×C47—81no—
119C22×C4×C47C22×C411yescharacteristic
120C22×C4×C47C22×C411yescharacteristic
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C2×D412yes—
124C22×C4×C47C2×D412yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2411yescharacteristic
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47—22no—
131C2×C22⋊D47—22no—
132C2×C22⋊D47—22no—
133C2×C22⋊D47—22no—
134C2×C22⋊D47—81no—
135C2×C22⋊D47—81no—
136C2×C22⋊D47—81no—
137C2×C22⋊D47—81no—
138C2×C22⋊D47—81no—
139C2×C22⋊D47—81no—
140C22×Dic47C22×C411yescharacteristic
141C22×Dic47C22×C411yescharacteristic
142C22×Dic47C22×C411yescharacteristic
143C22×Dic47C22×C411yescharacteristic
144C22×Dic47C22×C411yescharacteristic
145C2×D188—22no—
146C2×D188—22no—
147C2×D188—22no—
148C2×D188—42no—
149C2×D188—81no—
150C2×D188—81no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—42no—
155C2×C4×D47—81no—
156C2×C4×D47—81no—
157M16×C47—82no—
158C2×C8×C47—24no—
159C2×C8×C47—82no—
160C4⋊C4×C47C22⋊C414yes—
161C22⋊C4×C47C22⋊C414yes—
162C22⋊C4×C47C22⋊C414yes—
163C42×C47C2×D412yes—
164C42×C47C2×D412yes—
165C22⋊Dic47—22no—
166C22⋊Dic47—22no—
167(C2×D47)⋊C4—22no—
168(C2×D47)⋊C4—22no—
169(C2×D47)⋊C4—22no—
170(C2×D47)⋊C4—21no—
171(C2×D47)⋊C4—21no—
172(C2×D47)⋊C4—21no—
173(C2×D47)⋊C4—21no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176C4⋊Dic47—22no—
177C4⋊Dic47—22no—
178C4⋊Dic47—22no—
179Dic47⋊C4—22no—
180Dic47⋊C4—22no—
181Dic47⋊C4—22no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184C4×Dic47—22no—
185#10625329—82no—
186C2×C47⋊C8—24no—
187C2×C47⋊C8—82no—
188C23×C47—22no—
189C23×C47—22no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—41no—
194C23×C47C2×C22⋊C412yes—
195C23×C47C2×C22⋊C412yes—
196C23×C47C23×C411yescharacteristic
197C22×D47—21no—
198C22×D47—21no—
199C22×D47—21no—
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—22no—
203C22×D47—41no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209D4×C47—44no—
210C2×C4×C47—22no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47C2×C22⋊C412yes—
220C2×C4×C47C2×C22⋊C412yes—
221C2×C4×C47C2×C22⋊C412yes—
222C2×C4×C47C2×C22⋊C412yes—
223C2×C4×C47C22×D411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C22⋊D47—82no—
226C22⋊D47—82no—
227C22⋊D47—82no—
228C22⋊D47—82no—
229C22⋊D47—82no—
230C22⋊D47—82no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—22no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241D188—44no—
242D188—82no—
243D188—82no—
244C4×D47—44no—
245C4×D47—82no—
246C4×D47—82no—
247C8×C47—44no—
248C47⋊C8—44no—
249#17408—471nomaximal, Sylow
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—22no—
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—22no—
256C22×C47—22no—
257C22×C47—22no—
258C22×C47—82no—
259C22×C47—82no—
260C22×C47C22×C22⋊C411yescharacteristic
261C22×C47#56812yes—
262C2×D47—41no—
263C2×D47—41no—
264C2×D47—41no—
265C2×D47—41no—
266C2×D47—41no—
267C2×D47—41no—
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C2×D47—82no—
272C2×D47—82no—
273C2×D47—82no—
274C4×C47—22no—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—22no—
280Dic47—41no—
281Dic47—41no—
282Dic47—41no—
283Dic47—41no—
284Dic47—41no—
285C2×#540—471no—
286#2973—471no—
287#2973D4711yescharacteristic, complemented
288#1471—472no—
289#1471—472no—
290#1468—472no—
291#1468—472no—
292#1466—472no—
293#1464—472no—
294C2×C47—22no—
295C2×C47—42no—
296C2×C47—42no—
297C2×C47#287911yescharacteristic
298C2×C47#288311yescharacteristic
299C2×C47#288811yescharacteristic
300D47—81no—
301D47—81no—
302D47—81no—
303#540—944no—
304#540—944no—
305C2×#127—471no—
306C2×#125—471no—
307C2×#123—471no—
308C2×#123—471no—
309C2×#123—471no—
310C2×#123—471no—
311C2×#121—471no—
312C2×#121—471no—
313C2×#121—471no—
314C2×#121—471no—
315C2×#121—471no—
316C2×#121—471no—
317C2×C4×D4—471no—
318C2×C4×D4C2×D4711yescharacteristic
319C2×#117—471no—
320#435—24no—
321#435—944no—
322#432—472no—
323#432C2×D4712yes—
324#407—472no—
325#407C2×D4712yes—
326C2×C22⋊C8—472no—
327C2×C22⋊C8C2×D4712yes—
328#324—474no—
329#323—474no—
330#323—474no—
331#323—474no—
332C47#1740811yescharacteristic, complemented, Sylow
333C22×D4—471no—
334C22×D4—471no—
335C22×D4—471no—
336C22×D4—471no—
337C22×D4—471no—
338C22×D4—471no—
339C22×D4—471no—
340C22×D4—471no—
341C22×D4—471no—
342C22×D4C4×D4711yescharacteristic
343C23×C4—471no—
344C23×C4—471no—
345C23×C4—471no—
346C23×C4C22×D4711yescharacteristic
347C23×C4C22×D4711yescharacteristic
348C2×M16—22no—
349C2×M16—942no—
350C22×C8—22no—
351C22×C8—942no—
352#127—944no—
353#125—944no—
354#123—942no—
355#123—942no—
356#123—942no—
357#123—942no—
358#123—944no—
359#123—944no—
360#121—944no—
361#121—942no—
362#121—942no—
363#121—942no—
364#121—942no—
365#121—944no—
366#121—944no—
367#121—944no—
368C4×D4—942no—
369C4×D4—942no—
370C4×D4D18814yes—
371C4×D4C22⋊D4714yes—
372#117—942no—
373#117—942no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—471no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—471no—
379C2×C4⋊C4—471no—
380C2×C4⋊C4—471no—
381C2×C4⋊C4C4×D4711yescharacteristic
382C2×C22⋊C4—471no—
383C2×C22⋊C4—471no—
384C2×C22⋊C4—471no—
385C2×C22⋊C4—471no—
386C2×C22⋊C4—471no—
387C2×C22⋊C4—471no—
388C2×C22⋊C4—471no—
389C2×C22⋊C4—471no—
390C2×C22⋊C4C4×D4711yescharacteristic
391C2×C22⋊C4C4×D4711yescharacteristic
392C2×C42—471no—
393C2×C42C22×D4711yescharacteristic
394C4⋊C8—22no—
395C4⋊C8—942no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398C22⋊C8—474no—
399C22⋊C8—942no—
400C22⋊C8—942no—
401C22⋊C8C22×D4714yes—
402#97—22no—
403#97—942no—
404C24—471no—
405C24—471no—
406C24—471no—
407C24C2×C4×D4711yescharacteristic
408C24C2×C4×D4711yescharacteristic
409C2×D4—42no—
410C2×D4—942no—
411C2×D4—942no—
412C2×D4—942no—
413C2×D4—942no—
414C2×D4—942no—
415C2×D4—942no—
416C2×D4—942no—
417C2×D4—942no—
418C2×D4—942no—
419C2×D4—3761no—
420C2×D4—3761no—
421C2×D4—3761no—
422C2×D4—3761no—
423C2×D4—3761no—
424C2×D4—3761no—
425C2×D4—3761no—
426C2×D4—3761no—
427C2×D4—1882no—
428C2×D4(C2×D47)⋊C414yes—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—471no—
434C22×C4—471no—
435C22×C4—471no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—3761no—
440C22×C4—3761no—
441C22×C4—1882no—
442C22×C4C2×C4×D4711yescharacteristic
443C22×C4C2×C4×D4711yescharacteristic
444C22×C4C2×C4×D4711yescharacteristic
445C22×C4C2×C4×D4711yescharacteristic
446C22×C4C2×D18812yes—
447C22×C4C2×D18812yes—
448C22×C4C2×C22⋊D4712yes—
449C22×C4C2×C22⋊D4712yes—
450C22×C4C23×D4711yescharacteristic
451M16—82no—
452M16—3762no—
453C2×C8—24no—
454C2×C8—82no—
455C2×C8—944no—
456C2×C8—3762no—
457C4⋊C4—942no—
458C4⋊C4—942no—
459C4⋊C4—942no—
460C4⋊C4—942no—
461C4⋊C4—942no—
462C4⋊C4—942no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4(C2×D47)⋊C414yes—
466C22⋊C4—942no—
467C22⋊C4—942no—
468C22⋊C4—942no—
469C22⋊C4—942no—
470C22⋊C4—942no—
471C22⋊C4—941no—
472C22⋊C4—941no—
473C22⋊C4—941no—
474C22⋊C4—941no—
475C22⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4(C2×D47)⋊C414yes—
478C22⋊C4(C2×D47)⋊C414yes—
479C42—942no—
480C42C2×D18812yes—
481C42C2×C22⋊D4712yes—
482C23—22no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—942no—
489C23—942no—
490C23—942no—
491C23—941no—
492C23—941no—
493C23—941no—
494C23—1881no—
495C23—1881no—
496C23—1881no—
497C23—1881no—
498C23—1881no—
499C23—1881no—
500C23C2×(C2×D47)⋊C412yes—
501C23C2×(C2×D47)⋊C412yes—
502C23C22×C4×D4711yescharacteristic
503D4—44no—
504D4—3762no—
505D4—3762no—
506D4—3762no—
507D4—3762no—
508D4—3762no—
509D4—3762no—
510D4—3762no—
511D4—3762no—
512D4—1884no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—942no—
528C2×C4—3762no—
529C2×C4—3762no—
530C2×C4—1884no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4C2×(C2×D47)⋊C412yes—
536C2×C4C2×(C2×D47)⋊C412yes—
537C2×C4C2×(C2×D47)⋊C412yes—
538C2×C4C2×(C2×D47)⋊C412yes—
539C2×C4C22×C22⋊D4711yescharacteristic
540C2×C4C22×D18811yescharacteristic
541C8—44no—
542C8—1884no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—82no—
552C22—82no—
553C22—3762no—
554C22—3762no—
555C22—3762no—
556C22—1881no—
557C22—1881no—
558C22—1881no—
559C22—1881no—
560C22—1881no—
561C22—1881no—
562C22—1881no—
563C22—1881no—
564C22—1881no—
565C22C22×(C2×D47)⋊C411yescharacteristic
566C22#1568988912yes—
567C4—22no—
568C4—21no—
569C4—21no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—1881no—
574C4—1881no—
575C4—1881no—
576C4—1881no—
577C4—1881no—
578C2—22no—
579C2—42no—
580C2—42no—
581C2—3761no—
582C2—3761no—
583C2—3761no—
584C2#2025183211yescharacteristic
585C2#2025184811yescharacteristic
586C2#2025186611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2973C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689724C2
cosocleC22×C4×C47C24
hypercenter#2973D47
hypocenterC47#17408
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #20252417C2semidirect
3. #20241749C2semidirect
4. #20241747C2semidirect
5. #20241737C2semidirect
6. #20241734C2semidirect
7. #20241728C2semidirect
8. #20241720C2semidirect
9. C47×#2973C2semidirect
287. #2973D47semidirect
332. C47#17408semidirect

Maximal subgroups

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

subgroupindex
C2×#156897242
#202524172
#202417492
#202417472
#202417372
#202417342
#202417282
#202417202
C47×#29732
#1740847