Finite Group Databasebeta

← #26186419

Subgroups — #26186419

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253394C211yesmaximal, characteristic
2#20252484C211yesmaximal, characteristic, complemented
3#20252409C211yesmaximal, characteristic
4#20242245C211yesmaximal, characteristic, complemented
5#20242243C211yesmaximal, characteristic, complemented
6#20242226C211yesmaximal, characteristic, complemented
7#20242203C211yesmaximal, characteristic, complemented
8#20242197C211yesmaximal, characteristic, complemented
9SD16×C47⋊C8C211yesmaximal, characteristic, complemented
10#20242187C211yesmaximal, characteristic, complemented
11#20242165C211yesmaximal, characteristic, complemented
12#20241829C211yesmaximal, characteristic
13#20241807C211yesmaximal, characteristic, complemented
14#20241684C211yesmaximal, characteristic, complemented
15C47×#1582C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17C4×D4×D47C2211yescharacteristic
18#15689455C411yescharacteristic
19#15689452C411yescharacteristic
20#15689412C411yescharacteristic
21#15689411C411yescharacteristic
22#15689327C411yescharacteristic
23#15689326C411yescharacteristic
24#15689275C411yescharacteristic
25#15689272C411yescharacteristic
26#15689253C2211yescharacteristic, complemented
27#15689251—21no—
28#15689250—21no—
29Q8×C47⋊C8C2211yescharacteristic, complemented
30#15689247C2211yescharacteristic, complemented
31C4×#10625325C2211yescharacteristic
32C4×#10625336C2211yescharacteristic
33C4×#10625335C2211yescharacteristic
34C8×D188C2211yescharacteristic
35D4×C47⋊C8C2211yescharacteristic
36#15689188C2211yescharacteristic
37C8×C22⋊D47—21no—
38(C22⋊D47)⋊C8—21no—
39#15689185—21no—
40#15689183—21no—
41#15689179C2211yescharacteristic
42#15689175C2211yescharacteristic
43#15689174C2211yescharacteristic
44#15689174C2211yescharacteristic
45C2×(C2×D47)⋊C8—21no—
46C22⋊C8×D47—21no—
47C4×#10625324C2211yescharacteristic
48#15688875C2211yescharacteristic, complemented
49#15688875C2211yescharacteristic, complemented
50#15688874C2211yescharacteristic, complemented
51#15688855C2211yescharacteristic, complemented
52Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
53#15688853C2211yescharacteristic, complemented
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59C8×C47⋊C8C2211yescharacteristic, complemented
60C47×#446C2211yescharacteristic, complemented
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C2×D4×D47C2×C411yescharacteristic
68C22×C4×D47—21no—
69C2×#10625325C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625336C2×C411yescharacteristic
72C2×#10625324—21no—
73C22×C47⋊C8—21no—
74C2×C8×D47—21no—
75C2×C8×D47—21no—
76#13094023C2×C411yescharacteristic
77#13094022C2×C411yescharacteristic
78#13094014—21no—
79#13094004C2×C411yescharacteristic
80#13094002—21no—
81#13094000C2×C411yescharacteristic
82C4×Dic94—21no—
83C4×Dic94C2311yescharacteristic
84C4×D188C2311yescharacteristic
85D4×Dic47C2×C411yescharacteristic
86#13093986C2×C411yescharacteristic
87C4×C22⋊D47—21no—
88(C22⋊D47)⋊C4—21no—
89#13093981—21no—
90C4⋊C4×D47C2×C411yescharacteristic
91C22⋊C4×D47—21no—
92C42×D47C2311yescharacteristic
93#13093956C2×C411yescharacteristic
94#13093955C2×C411yescharacteristic
95#13093955C2×C411yescharacteristic
96C4⋊(C47⋊C8)—21no—
97C4⋊(C47⋊C8)C2311yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8C2×C411yescharacteristic
102Dic47⋊C8C2×C411yescharacteristic
103Dic47⋊C8D411yescharacteristic
104Dic47⋊C8D411yescharacteristic
105#13093949C2×C411yescharacteristic
106#13093948C2×C411yescharacteristic
107#13093947C2×C411yescharacteristic
108#13093946C2×C411yescharacteristic
109#13093945C2×C411yescharacteristic
110#13093944C2×C411yescharacteristic
111C22⋊(C47⋊C8)—21no—
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8C2×C411yescharacteristic
117(C2×D47)⋊C8C2×C411yescharacteristic
118(C2×D47)⋊C8D411yescharacteristic
119(C2×D47)⋊C8D411yescharacteristic
120#13093934—21no—
121#13093934—21no—
122#13093934—21no—
123C4×C47⋊C8—21no—
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×SD16×C47C2×C411yescharacteristic
130C22×C8×C47—21no—
131C4×Q8×C47C2311yescharacteristic
132C4×D4×C47C2311yescharacteristic
133#106×C47C2×C411yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139C22⋊C8×C47—21no—
140#97×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C23×D47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C2×C22⋊D47—21no—
149C22×Dic47—21no—
150D4×D47—22no—
151D4×D47—22no—
152C2×D188C22×C411yescharacteristic
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—81no—
157C2×C4×D47—81no—
158C2×C4×D47C22×C411yescharacteristic
159C2×C4×D47C2×D411yescharacteristic
160C2×C4×D47#4111yescharacteristic
161C2×Dic94—21no—
162C2×Dic94C22×C411yescharacteristic
163SD16×C47—22no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—81no—
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C22⋊C4×C47—21no—
176C42×C47—21no—
177C42×C47C2411yescharacteristic
178C22⋊Dic47—21no—
179#10625336—22no—
180#10625335—22no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47C22×C411yescharacteristic
187C4⋊Dic47C22×C411yescharacteristic
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194C4×Dic47—21no—
195C4×Dic47C22×C411yescharacteristic
196C4×Dic47C2×D411yescharacteristic
197C4×Dic47#4111yescharacteristic
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—81no—
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206#10625325—22no—
207#10625324—42no—
208C8×D47—81no—
209C8×D47—81no—
210C23×C47—21no—
211C22×D47—21no—
212C22×D47—24no—
213C22×D47—81no—
214C22×D47—81no—
215C22×D47C4×D411yescharacteristic
216Q8×C47—21no—
217Q8×C47—21no—
218D4×C47—21no—
219D4×C47#13112yes—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47C23×C411yescharacteristic
226C2×C4×C47C22×D411yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C22⋊D47—24no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—81no—
233C2×Dic47C4×D411yescharacteristic
234C2×Dic47C4×D411yescharacteristic
235C2×Dic47C4×D411yescharacteristic
236D188—21no—
237D188#13112yes—
238C4×D47—21no—
239C4×D47—21no—
240C4×D47—21no—
241C4×D47—21no—
242C4×D47—41no—
243C4×D47—41no—
244C4×D47—41no—
245C4×D47—81no—
246C4×D47—81no—
247Dic94—21no—
248Dic94—21no—
249Dic94—81no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257C47⋊C8—22no—
258C47⋊C8—21no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—41no—
263C47⋊C8—41no—
264#17924—471nomaximal, Sylow
265C22×C47—22no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47C2×C4×D411yescharacteristic
269C2×D47—21no—
270C2×D47—22no—
271C2×D47—21no—
272C2×D47—21no—
273C2×D47—41no—
274C2×D47—41no—
275C2×D47—84no—
276C4×C47—21no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47C2×#13111yescharacteristic
281C4×C47C2×#13111yescharacteristic
282C4×C47#57711yescharacteristic
283C4×C47#57711yescharacteristic
284Dic47—21no—
285Dic47—21no—
286Dic47—21no—
287Dic47—41no—
288Dic47—41no—
289Dic47—41no—
290#3101—471no—
291#2985—471no—
292#2972—471no—
293#1585—471no—
294#1585—471no—
295#1582—471no—
296#1582D4711yescharacteristic, complemented
297SD16⋊C8—471no—
298SD16⋊C8—471no—
299C8×SD16—471no—
300C8×SD16—471no—
301#1572—471no—
302#1490—471no—
303#1485—471no—
304#1453—471no—
305C2×C47—42no—
306C2×C47#292911yescharacteristic
307C2×C47#294911yescharacteristic
308C2×C47#295611yescharacteristic
309D47—41no—
310D47—42no—
311#533—471no—
312C2×C4×D4—471no—
313#483—471no—
314#483—471no—
315#476—471no—
316#476—471no—
317#461—471no—
318#461—471no—
319#450—471no—
320#450—471no—
321#446—471no—
322#446—941no—
323#446—941no—
324#446C2×D4711yescharacteristic, complemented
325C8×Q8—471no—
326C8×Q8—471no—
327C4×SD16—471no—
328C4×SD16—471no—
329C4×SD16—471no—
330C4×SD16C2×D4711yescharacteristic
331C8×D4—471no—
332C8×D4—471no—
333C8×D4—471no—
334C8×D4—941no—
335C8×D4—941no—
336C8×D4C2×D4711yescharacteristic
337#433—941no—
338#433—941no—
339#432—471no—
340#431—471no—
341#431—471no—
342#431—471no—
343C2×C22⋊C8—941no—
344C2×C22⋊C8—941no—
345C4×M16—471no—
346#335—471no—
347#335—471no—
348#334—471no—
349#334C2×D4711yescharacteristic, complemented
350Q8⋊C8—471no—
351Q8⋊C8—471no—
352Q8⋊C8—471no—
353Q8⋊C8C2×D4711yescharacteristic, complemented
354D4⋊C8—471no—
355D4⋊C8—471no—
356D4⋊C8—471no—
357D4⋊C8C2×D4711yescharacteristic
358#322—471no—
359#322—471no—
360#322C2×D4711yescharacteristic, complemented
361C82—471no—
362C47#1792411yescharacteristic, complemented, Sylow
363C22×D4—471no—
364C23×C4—941no—
365C2×SD16—471no—
366C2×SD16—471no—
367C2×SD16—471no—
368C2×SD16C4×D4711yescharacteristic
369C2×M16—941no—
370C22×C8—21no—
371C22×C8—941no—
372C22×C8—941no—
373C22×C8—941no—
374C4⋊Q8—471no—
375C4⋊Q8—471no—
376#125—941no—
377C22⋊Q8—471no—
378C22⋊Q8—471no—
379C22⋊Q8—941no—
380C4×Q8—471no—
381C4×Q8—941no—
382C4×Q8C22×D4711yescharacteristic
383C4×D4—471no—
384C4×D4—471no—
385C4×D4—471no—
386C4×D4—941no—
387C4×D4—941no—
388C4×D4C22×D4711yescharacteristic
389#117—941no—
390C2×C4⋊C4—471no—
391C2×C22⋊C4—941no—
392C2×C42—471no—
393#106—471no—
394#106—471no—
395#106—471no—
396#106C4×D4711yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—471no—
399C4⋊C8—471no—
400C4⋊C8—471no—
401C4⋊C8—471no—
402C4⋊C8—471no—
403C4⋊C8—471no—
404C4⋊C8—941no—
405C4⋊C8—941no—
406C4⋊C8—941no—
407C4⋊C8C22×D4711yescharacteristic
408C4⋊C8C22×D4711yescharacteristic
409#103—471no—
410#103—471no—
411#103—471no—
412#103C4×D4711yescharacteristic
413#102—471no—
414#102—471no—
415#102—471no—
416#102C4×D4711yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—471no—
419C22⋊C8—471no—
420C22⋊C8—471no—
421C22⋊C8—471no—
422C22⋊C8—941no—
423C22⋊C8—941no—
424C22⋊C8—941no—
425C22⋊C8—941no—
426C22⋊C8—941no—
427#97—21no—
428#97—941no—
429#97—941no—
430#97—941no—
431C4×C8—471no—
432C4×C8—471no—
433C4×C8—471no—
434C4×C8—941no—
435C4×C8—941no—
436C4×C8—941no—
437C4×C8C22×D4711yescharacteristic
438C4×C8C22×D4711yescharacteristic
439C4×C8C22×D4711yescharacteristic
440C24—941no—
441C2×Q8—471no—
442C2×Q8—941no—
443C2×Q8C2×C4×D4711yescharacteristic
444C2×D4—471no—
445C2×D4—941no—
446C2×D4—942no—
447C2×D4—942no—
448C2×D4C2×C4×D4711yescharacteristic
449C22×C4—21no—
450C22×C4—471no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—3761no—
458C22×C4—3761no—
459SD16—22no—
460SD16—942no—
461SD16—942no—
462SD16—942no—
463M16—1882no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—471no—
469C2×C8—471no—
470C2×C8—471no—
471C2×C8—471no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—3761no—
476C2×C8—3761no—
477C2×C8—3761no—
478C2×C8C2×C4×D4711yescharacteristic
479C2×C8C2×C4×D4711yescharacteristic
480C2×C8D4×D4711yescharacteristic
481C2×C8D4×D4711yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—471no—
484C4⋊C4—471no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4C2×C4×D4711yescharacteristic
493C4⋊C4C2×C4×D4711yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—941no—
496C22⋊C4—941no—
497C22⋊C4—941no—
498C22⋊C4—941no—
499C22⋊C4—941no—
500C42—21no—
501C42—471no—
502C42—471no—
503C42—471no—
504C42—941no—
505C42C23×D4711yescharacteristic
506C23—21no—
507C23—471no—
508C23—944no—
509C23—941no—
510C23—3761no—
511C23—3761no—
512Q8—21no—
513Q8—21no—
514Q8—941no—
515Q8—941no—
516Q8—3761no—
517D4—21no—
518D4—472no—
519D4—944no—
520D4—941no—
521D4#1309403212yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—471no—
528C2×C4—471no—
529C2×C4—471no—
530C2×C4—941no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—941no—
536C2×C4—941no—
537C2×C4—3761no—
538C2×C4—3761no—
539C2×C4—3761no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4C22×C4×D4711yescharacteristic
544C2×C4C2×D4×D4711yescharacteristic
545C2×C4#41×D4711yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—942no—
554C8—941no—
555C8—941no—
556C8—941no—
557C8—941no—
558C8—1881no—
559C8—1881no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—941no—
564C22—941no—
565C22—941no—
566C22—942no—
567C22—3764no—
568C22—1881no—
569C22—1881no—
570C22C4×D4×D4711yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—941no—
576C4—941no—
577C4—941no—
578C4—1881no—
579C4—1881no—
580C4—1881no—
581C4#131×D4711yescharacteristic
582C4C2×#1309403211yescharacteristic
583C4#1568992911yescharacteristic
584C4#1568993011yescharacteristic
585C2—42no—
586C2—1881no—
587C2—1882no—
588C2#2025207911yescharacteristic
589C2#2025224211yescharacteristic
590C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1582C2
socleC22×C47C2×C4×D4
prime radicalC2×D4×D47C2×C4
cosocleC42×C47C24
hypercenter#1582D47
hypocenterC47#17924
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #20252484C2semidirect
4. #20242245C2semidirect
5. #20242243C2semidirect
6. #20242226C2semidirect
7. #20242203C2semidirect
8. #20242197C2semidirect
9. SD16×C47⋊C8C2semidirect
10. #20242187C2semidirect
11. #20242165C2semidirect
13. #20241807C2semidirect
14. #20241684C2semidirect
15. C47×#1582C2semidirect
26. #15689253C22semidirect
29. Q8×C47⋊C8C22semidirect
30. #15689247C22semidirect
48. #15688875C22semidirect
49. #15688875C22semidirect
50. #15688874C22semidirect
51. #15688855C22semidirect
52. Q8⋊(C47⋊C8)C22semidirect
53. #15688853C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. C8×C47⋊C8C22semidirect
60. C47×#446C22semidirect
63. C47×#334C22semidirect
64. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
296. #1582D47semidirect
324. #446C2×D47semidirect
349. #334C2×D47semidirect
353. Q8⋊C8C2×D47semidirect
360. #322C2×D47semidirect
362. C47#17924semidirect

Maximal subgroups

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

subgroupindex
#202533942
#202524842
#202524092
#202422452
#202422432
#202422262
#202422032
#202421972
SD16×C47⋊C82
#202421872
#202421652
#202418292
#202418072
#202416842
C47×#15822
#1792447