Finite Group Databasebeta

← #26123206

Subgroups — #26123206

Order 12032.

1146 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689146C211yesmaximal, characteristic, complemented
2C22×#13093940C211yesmaximal, characteristic
3C22×#13093940C211yesmaximal, characteristic
4C2×#15689024C211yesmaximal, characteristic
5C2×#15688892C211yesmaximal, characteristic, complemented
6#20243081C211yesmaximal, characteristic, complemented
7C2×C47×#343C211yesmaximal, characteristic, complemented
8C23×D188C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×(C2×D47)⋊C4C414yes—
12C22×C4×Dic47C2211yescharacteristic
13#15689146—22no—
14#15689146—22no—
15C2×Dic47⋊C8—22no—
16C2×#13093940—22no—
17C2×#13093940—22no—
18C2×#13093940—22no—
19C2×#13093940—22no—
20C2×#13093940—22no—
21C2×#13093940—22no—
22#15689024—21no—
23#15689024—21no—
24#15689024—22no—
25#15688892—22no—
26#15688877—21no—
27#15688877—21no—
28C22×M16×C47C2211yescharacteristic
29C22×M16×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C47×#343—22no—
32C24×D47C2×C412yes—
33C22×D188—21no—
34C22×D188—21no—
35C22×D188—21no—
36C22×D188—21no—
37C22×D188—21no—
38C22×D188—21no—
39C22×D188—21no—
40C22×D188—21no—
41C22×D188—21no—
42C22×D188—21no—
43C22×D188—21no—
44C22×D188—21no—
45C22×D188D412yes—
46C22×D188Q812yes—
47C23×Dic47C2×C412yes—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329D412yes—
59C2×#10625329D412yes—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C2×(C2×D47)⋊C4—24no—
63C2×(C2×D47)⋊C4—24no—
64C2×(C2×D47)⋊C4—48no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47D411yescharacteristic
70C2×C4×Dic47D411yescharacteristic
71C2×C4×Dic47D412yes—
72Dic47⋊C8—28no—
73#13093940—28no—
74#13093940—28no—
75C23×C4×C47C2×C412yes—
76C23×C4×C47C2311yescharacteristic
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47—21no—
83C2×M16×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47D412yes—
88C2×M16×C47D412yes—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C24×C47C22×C411yescharacteristic
98C23×D47—22no—
99C23×D47—22no—
100C23×D47—22no—
101C23×D47—22no—
102C23×D47—22no—
103C23×D47—22no—
104C23×D47—44no—
105C23×D47—44no—
106C23×D47C4⋊C414yes—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—44no—
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×Q811yescharacteristic
119C22×C4×C47#4111yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—24no—
128C22×Dic47—42no—
129C22×Dic47C22⋊C412yes—
130C22×Dic47C22⋊C412yes—
131C2×D188—22no—
132C2×D188—22no—
133C2×D188—22no—
134C2×D188—22no—
135C2×D188—22no—
136C2×D188—22no—
137C2×D188—22no—
138C2×D188—22no—
139C2×D188—22no—
140C2×D188—22no—
141C2×D188—22no—
142C2×D188—22no—
143C2×D188—41no—
144C2×D188—41no—
145C2×D188—41no—
146C2×D188—41no—
147C2×D188—41no—
148C2×D188—41no—
149C2×D188—41no—
150C2×D188—41no—
151C2×D188—41no—
152C2×D188—41no—
153C2×D188—41no—
154C2×D188—41no—
155C2×D188—41no—
156C2×D188—41no—
157C2×D188—41no—
158C2×D188—41no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47—22no—
163M16×C47—41no—
164M16×C47—41no—
165M16×C47—41no—
166M16×C47—41no—
167C2×C8×C47—22no—
168C2×C8×C47—22no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C2×C8×C47—41no—
172C2×C8×C47—41no—
173C4⋊C4×C47—41no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47—41no—
176C4⋊C4×C47—41no—
177(C2×D47)⋊C4—48no—
178(C2×D47)⋊C4—48no—
179C4×Dic47—22no—
180C4×Dic47—21no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—21no—
184C4×Dic47—22no—
185#10625329—22no—
186#10625329—22no—
187#10625329—22no—
188#10625329—22no—
189#10625329—41no—
190#10625329—41no—
191#10625329—41no—
192#10625329—41no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C2×C47⋊C8—41no—
198C2×C47⋊C8—41no—
199C23×C47—22no—
200C23×C47—22no—
201C23×C47C2×C22⋊C411yescharacteristic
202C23×C47C2×C4⋊C411yescharacteristic
203C23×C47#11711yescharacteristic
204C23×C47C4×D411yescharacteristic
205C23×C47C4×D411yescharacteristic
206C23×C47C4×D411yescharacteristic
207C23×C47C4×D411yescharacteristic
208C22×D47—24no—
209C22×D47—24no—
210C22×D47—24no—
211C22×D47—48no—
212C22×D47—42no—
213C22×D47—42no—
214C22×D47—42no—
215C22×D47—42no—
216C22×D47—44no—
217C22×D47—44no—
218C22×D47—48no—
219C22×D47—84no—
220C22×D47—84no—
221C22×D47—82no—
222C22×D47—82no—
223C22×D47—82no—
224C22×D47—82no—
225C2×C4×C47—42no—
226C2×C4×C47—44no—
227C2×C4×C47—82no—
228C2×C4×C47—82no—
229C2×C4×C47#12011yescharacteristic
230C2×C4×C47#12011yescharacteristic
231C2×C4×C47#12011yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12111yescharacteristic
236C2×C4×C47#12111yescharacteristic
237C2×C4×C47#12111yescharacteristic
238C2×C4×C47#12111yescharacteristic
239C2×C4×C47#12111yescharacteristic
240C2×C4×C47C22⋊Q811yescharacteristic
241C2×C4×C47C22⋊Q811yescharacteristic
242C2×C4×C47C22⋊Q811yescharacteristic
243C2×C4×C47C22⋊Q811yescharacteristic
244C2×C4×C47C22⋊Q811yescharacteristic
245C2×C4×C47C22⋊Q811yescharacteristic
246C2×C4×C47#12311yescharacteristic
247C2×C4×C47#12311yescharacteristic
248C2×C4×C47#12311yescharacteristic
249C2×C4×C47#12311yescharacteristic
250C2×C4×C47#12311yescharacteristic
251C2×C4×C47#12411yescharacteristic
252C2×C4×C47#12411yescharacteristic
253C2×C4×C47#12411yescharacteristic
254C2×C4×C47#12611yescharacteristic
255C2×C4×C47#12611yescharacteristic
256C2×C4×C47#12711yescharacteristic
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—44no—
263C2×Dic47—44no—
264C2×Dic47#10014yescomplemented
265D188—42no—
266D188—42no—
267D188—42no—
268D188—42no—
269D188—42no—
270D188—42no—
271D188—42no—
272D188—42no—
273C8×C47—42no—
274C8×C47—42no—
275C47⋊C8—42no—
276C47⋊C8—42no—
277#11044—471nomaximal, Sylow
278C22×C47—22no—
279C22×C47—22no—
280C22×C47—22no—
281C22×C47—22no—
282C22×C47—21no—
283C22×C47—21no—
284C22×C47—21no—
285C22×C47—21no—
286C22×C47#38011yescharacteristic
287C22×C47#38511yescharacteristic
288C22×C47#38511yescharacteristic
289C22×C47#38611yescharacteristic
290C22×C47#38811yescharacteristic
291C22×C47#38811yescharacteristic
292C22×C47#39011yescharacteristic
293C22×C47C2×#10012yes—
294C22×C47#41312yes—
295C2×D47—48no—
296C2×D47—44no—
297C2×D47—84no—
298C2×D47—84no—
299C2×D47—84no—
300C2×D47—82no—
301C2×D47—82no—
302C2×D47—84no—
303C2×D47—84no—
304C4×C47—82no—
305C4×C47#39211yescharacteristic
306C4×C47#39311yescharacteristic
307C4×C47#39411yescharacteristic
308C4×C47#39411yescharacteristic
309C4×C47#39611yescharacteristic
310C4×C47#39611yescharacteristic
311C4×C47#39711yescharacteristic
312C4×C47#39911yescharacteristic
313Dic47—24no—
314Dic47—42no—
315C2×#423—471no—
316C22×#100—471no—
317C22×#100—471no—
318C2×#390—471no—
319C2×#343—471no—
320C2×#343D4711yescharacteristic, complemented
321#1728—471no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—21no—
326C2×C47#143911yescharacteristic
327C2×C47#180012yes—
328C2×C47#190012yes—
329C2×C47#196511yescharacteristic
330C2×C47#196711yescharacteristic
331D47—84no—
332C23×D4—471no—
333C22×M16—471no—
334C22×M16—471no—
335C22×M16C2×D4711yescharacteristic
336C22×M16C2×D4711yescharacteristic
337C22×C4⋊C4C2×D4711yescharacteristic
338C22×C22⋊C4—474no—
339C22×C42—471no—
340#423—942no—
341#423—942no—
342C2×C4⋊C8—942no—
343C2×#100—942no—
344C2×#100—942no—
345C2×#100—942no—
346C2×#100—942no—
347C2×#100—942no—
348C2×#100—942no—
349#390—941no—
350#390—941no—
351#390—942no—
352#343—22no—
353#343—942no—
354#336—941no—
355#336—941no—
356C47#1104411yescharacteristic, complemented, Sylow
357C25—472no—
358C22×D4—472no—
359C22×D4—472no—
360C22×D4—941no—
361C22×D4—941no—
362C22×D4—941no—
363C22×D4—941no—
364C22×D4—941no—
365C22×D4—941no—
366C22×D4—941no—
367C22×D4—941no—
368C22×D4—941no—
369C22×D4—941no—
370C22×D4—941no—
371C22×D4—941no—
372C23×C4—472no—
373C23×C4C4×D4712yes—
374C23×C4C22×D4711yescharacteristic
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—472no—
386C2×M16—472no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16—941no—
390C2×M16—941no—
391C2×M16—941no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16—941no—
396C2×M16—941no—
397C2×M16D18812yes—
398C2×M16C22⋊D4712yes—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—941no—
402C22×C8—941no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C22⋊C4—944no—
410C2×C22⋊C4—944no—
411C2×C22⋊C4—1888no—
412C2×C42—471no—
413C2×C42—471no—
414C2×C42—472no—
415C2×C42—941no—
416C2×C42—941no—
417C2×C42—941no—
418C2×C42—941no—
419C4⋊C8—948no—
420#100—948no—
421#100—948no—
422C24—474no—
423C24—942no—
424C24—942no—
425C24—942no—
426C24—942no—
427C24—942no—
428C24—942no—
429C24—1884no—
430C24—1884no—
431C24C2×C4×D4711yescharacteristic
432C2×D4—942no—
433C2×D4—942no—
434C2×D4—942no—
435C2×D4—942no—
436C2×D4—942no—
437C2×D4—942no—
438C2×D4—942no—
439C2×D4—942no—
440C2×D4—942no—
441C2×D4—942no—
442C2×D4—942no—
443C2×D4—942no—
444C2×D4—1881no—
445C2×D4—1881no—
446C2×D4—1881no—
447C2×D4—1881no—
448C2×D4—1881no—
449C2×D4—1881no—
450C2×D4—1881no—
451C2×D4—1881no—
452C2×D4—1881no—
453C2×D4—1881no—
454C2×D4—1881no—
455C2×D4—1881no—
456C2×D4—1881no—
457C2×D4—1881no—
458C2×D4—1881no—
459C2×D4—1881no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—44no—
464C22×C4—472no—
465C22×C4—472no—
466C22×C4—944no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—1882no—
470C22×C4C2×D18811yescharacteristic
471C22×C4#1062535011yescharacteristic
472C22×C4#1062535011yescharacteristic
473C22×C4#1062535011yescharacteristic
474C22×C4#1062535011yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4D4×D4711yescharacteristic
477C22×C4D4×D4711yescharacteristic
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4711yescharacteristic
480C22×C4#1062535211yescharacteristic
481C22×C4Q8×D4711yescharacteristic
482C22×C4#1062535411yescharacteristic
483C22×C4C2×C22⋊D4711yescharacteristic
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—41no—
489M16—41no—
490M16—41no—
491M16—41no—
492M16—942no—
493M16—942no—
494M16—942no—
495M16—942no—
496M16—1881no—
497M16—1881no—
498M16—1881no—
499M16—1881no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—942no—
507C2×C8—942no—
508C2×C8—1881no—
509C2×C8—1881no—
510C2×C8—1881no—
511C2×C8—1881no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C22⋊C4—1888no—
517C22⋊C4—1888no—
518C42—942no—
519C42—941no—
520C42—941no—
521C42—941no—
522C42—941no—
523C42—942no—
524C23—22no—
525C23—22no—
526C23—944no—
527C23—944no—
528C23—944no—
529C23—3762no—
530C23—3762no—
531C23—3762no—
532C23—3762no—
533C23—3764no—
534C23—3764no—
535C23—1888no—
536C23—1888no—
537C23—1882no—
538C23—1882no—
539C23—1882no—
540C23—1882no—
541C23—1884no—
542C23—1884no—
543C23C22⋊C4×D4711yescharacteristic
544C23C4⋊C4×D4711yescharacteristic
545C23#1309398111yescharacteristic
546C23(C22⋊D47)⋊C411yescharacteristic
547C23C4×C22⋊D4711yescharacteristic
548C23#1309398611yescharacteristic
549C23C4×D18811yescharacteristic
550D4—1882no—
551D4—1882no—
552D4—1882no—
553D4—1882no—
554D4—1882no—
555D4—1882no—
556D4—1882no—
557D4—1882no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—474no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—1884no—
569C2×C4—1884no—
570C2×C4#1309399211yescharacteristic
571C2×C4#1309399411yescharacteristic
572C2×C4#1309399411yescharacteristic
573C2×C4#1309399611yescharacteristic
574C2×C4#1309399711yescharacteristic
575C2×C4#1309399711yescharacteristic
576C2×C4#1309399711yescharacteristic
577C2×C4#1309399711yescharacteristic
578C2×C4#1309399711yescharacteristic
579C2×C4#1309399811yescharacteristic
580C2×C4#1309399911yescharacteristic
581C2×C4#1309400011yescharacteristic
582C2×C4#1309400211yescharacteristic
583C2×C4#1309400211yescharacteristic
584C2×C4#1309400211yescharacteristic
585C2×C4#1309400211yescharacteristic
586C2×C4#1309400411yescharacteristic
587C2×C4#1309400611yescharacteristic
588C2×C4#1309400711yescharacteristic
589C2×C4#1309400911yescharacteristic
590C2×C4#1309400911yescharacteristic
591C2×C4#1309400911yescharacteristic
592C2×C4#1309401011yescharacteristic
593C2×C4#1309401011yescharacteristic
594C2×C4#1309401211yescharacteristic
595C2×C4#1309401811yescharacteristic
596C2×C4#1309401911yescharacteristic
597C2×C4#1309402011yescharacteristic
598C8—42no—
599C8—42no—
600C8—1882no—
601C8—1882no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—3764no—
611C22—3764no—
612C22—3764no—
613C22—3764no—
614C22—3762no—
615C22—3762no—
616C22—3764no—
617C22—1888no—
618C22—1884no—
619C22#1568898211yescharacteristic
620C22#1568899411yescharacteristic
621C22#1568899711yescharacteristic
622C22#1568900111yescharacteristic
623C22#1568901211yescharacteristic
624C22#1568901411yescharacteristic
625C22#1568902311yescharacteristic
626C22#100×D4712yes—
627C22#1568910612yes—
628C4—82no—
629C4—944no—
630C4—1882no—
631C4#1568903211yescharacteristic
632C4#1568903611yescharacteristic
633C4#1568903811yescharacteristic
634C4#1568904111yescharacteristic
635C4#1568904511yescharacteristic
636C4#1568904711yescharacteristic
637C4#1568905211yescharacteristic
638C4#1568905811yescharacteristic
639C2—21no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—3764no—
644C2#2024163211yescharacteristic
645C2#2024337912yes—
646C2#2024385012yes—
647C2#2024422611yescharacteristic
648C2#2024423611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#343C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D188C22
cosocleC23×C4×C47C23
hypercenterC2×#343D47
hypocenterC47#11044
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
1. C2×#15689146C2semidirect
5. C2×#15688892C2semidirect
6. #20243081C2semidirect
7. C2×C47×#343C2semidirect
264. C2×Dic47#100semidirect
320. C2×#343D47semidirect
356. C47#11044semidirect

Maximal subgroups

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

subgroupindex
C2×#156891462
C22×#130939402
C2×#156890242
C2×#156888922
#202430812
C2×C47×#3432
#1104447