Finite Group Databasebeta

← #26185756

Subgroups — #26185756

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252498C211yesmaximal, characteristic, complemented
2#20252495C211yesmaximal, characteristic, complemented
3C4×#13094045C211yesmaximal, characteristic
4#20242202C211yesmaximal, characteristic, complemented
5SD16⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#20242199C211yesmaximal, characteristic, complemented
7C8×#10625337C211yesmaximal, characteristic, complemented
8#20242192C211yesmaximal, characteristic, complemented
9C8×#10625334C211yesmaximal, characteristic, complemented
10#20242180C211yesmaximal, characteristic, complemented
11#335×D47C211yesmaximal, characteristic, complemented
12#20241774C211yesmaximal, characteristic, complemented
13#20241772C211yesmaximal, characteristic, complemented
14#20241673C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#13094045C411yescharacteristic
17C4×#10625354C2211yescharacteristic
18C4×#10625352C2211yescharacteristic
19Q8×C47⋊C8C2211yescharacteristic
20C8×Dic94C2211yescharacteristic
21#15689247C2211yescharacteristic
22C4×#10625337C2211yescharacteristic
23#15689215C411yescharacteristic
24C4×#10625325C2211yescharacteristic
25SD16×Dic47C411yescharacteristic
26#15689210C411yescharacteristic
27C4×#10625334C2211yescharacteristic
28#15689203C411yescharacteristic
29C8×D188—21no—
30C8×D188C2211yescharacteristic
31D4×C47⋊C8C2211yescharacteristic
32#15689188—21no—
33#15689188C2211yescharacteristic
34C8×C22⋊D47—21no—
35(C22⋊D47)⋊C8—21no—
36#15689174—21no—
37#15689174C2211yescharacteristic
38#15689174C2211yescharacteristic
39#15689173—21no—
40#15689158C411yescharacteristic
41C2×Dic47⋊C8—21no—
42C4⋊C8×D47—21no—
43C4⋊C8×D47C2211yescharacteristic
44C4⋊C8×D47C2211yescharacteristic
45#15689118C411yescharacteristic
46#15689116C411yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688844C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625354C2×C411yescharacteristic
68C2×#10625352C2×C411yescharacteristic
69#13094045C818yescomplemented
70C2×#10625337C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625334C2×C411yescharacteristic
73C22×C47⋊C8—21no—
74C2×C8×D47—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47C2×C411yescharacteristic
79C2×C8×D47C2×C411yescharacteristic
80Q8×Dic47C2×C411yescharacteristic
81C4×Dic94C2311yescharacteristic
82#13093989C2×C411yescharacteristic
83C4×D188—21no—
84C4×D188C2311yescharacteristic
85D4×Dic47C2×C411yescharacteristic
86#13093986—21no—
87#13093986C2×C411yescharacteristic
88C4×C22⋊D47—21no—
89(C22⋊D47)⋊C4—21no—
90#13093982—21no—
91#13093982C2×C411yescharacteristic
92#13093982C2×C411yescharacteristic
93#13093980—21no—
94C2×C4×Dic47—21no—
95C42×D47—21no—
96C42×D47C2311yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093957C2×C411yescharacteristic
99#13093956C2×C411yescharacteristic
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8D411yescharacteristic
109Dic47⋊C8D411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093948C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116C22⋊(C47⋊C8)—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8D411yescharacteristic
121(C2×D47)⋊C8D411yescharacteristic
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47C2×C411yescharacteristic
129C8×Dic47C2×C411yescharacteristic
130C2×SD16×C47C2×C411yescharacteristic
131C22×C8×C47—21no—
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#106×C47C2×C411yescharacteristic
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C2×C22⋊D47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151#10625354—22no—
152#10625354C2×C814yescomplemented
153#10625352—22no—
154#10625352C2×C814yescomplemented
155C2×D188—21no—
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47C22×C411yescharacteristic
161C2×C4×D47C2×D411yescharacteristic
162C2×C4×D47#4111yescharacteristic
163C2×Dic94C22×C411yescharacteristic
164SD16×C47C2×C814yescomplemented
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—81no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C4⋊C4×C47—21no—
174C4⋊C4×C47C22×C411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C22⋊C4×C47—21no—
177C42×C47—21no—
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180#10625337C2×C814yescomplemented
181#10625334C2×C814yescomplemented
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47C22×C411yescharacteristic
197C4×Dic47C2×D411yescharacteristic
198C4×Dic47#4111yescharacteristic
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—81no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207#10625325C2×C814yescomplemented
208C8×D47—22no—
209C8×D47—81no—
210C8×D47—81no—
211C8×D47—81no—
212C8×D47—81no—
213C8×D47C2×C814yescomplemented
214C23×C47—21no—
215C22×D47—21no—
216C22×D47C4×D411yescharacteristic
217Q8×C47—21no—
218Q8×C47C22×C812yes—
219D4×C47—21no—
220D4×C47C22×C812yes—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47C23×C411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C22⋊D47—24no—
230C2×Dic47—21no—
231C2×Dic47—24no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—81no—
235C2×Dic47C4×D411yescharacteristic
236C2×Dic47C4×D411yescharacteristic
237C2×Dic47C4×D411yescharacteristic
238D188—24no—
239D188—21no—
240D188C22×C812yes—
241C4×D47—21no—
242C4×D47—21no—
243C4×D47—24no—
244C4×D47—41no—
245C4×D47—41no—
246C4×D47—41no—
247C4×D47—81no—
248C4×D47C22×C812yes—
249C4×D47#13112yes—
250Dic94—21no—
251Dic94C22×C812yes—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47C22×C812yes—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—41no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265C47⋊C8C22×C812yes—
266#17857—471nomaximal, Sylow
267C22×C47—22no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47C2×C4×D411yescharacteristic
271C2×D47—21no—
272C2×D47—21no—
273C2×D47—22no—
274C2×D47—41no—
275C2×D47—41no—
276C2×D47C8×D412yes—
277C4×C47—22no—
278C4×C47—21no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47C23×C811yescharacteristic
282C4×C47C2×#13111yescharacteristic
283C4×C47#57611yescharacteristic
284C4×C47#57811yescharacteristic
285Dic47—22no—
286Dic47—21no—
287Dic47—21no—
288Dic47—41no—
289Dic47—41no—
290Dic47C8×D412yes—
291#2988—471no—
292#2988—471no—
293C4×#135—471no—
294SD16⋊C8—471no—
295SD16⋊C8—471no—
296SD16⋊C8—471no—
297SD16⋊C8D4711yescharacteristic, complemented
298C8×Q16—471no—
299C8×Q16—471no—
300C8×D8—471no—
301C8×D8—471no—
302C2×#335—471no—
303#1477—471no—
304#1477—471no—
305#1450—471no—
306C2×C47—42no—
307C2×C47C2×C8×D411yescharacteristic
308C2×C47#295111yescharacteristic
309C2×C47#295711yescharacteristic
310D47—22no—
311D47—42no—
312C2×#135—471no—
313C4×#41—471no—
314C4×#41—471no—
315C8×Q8—471no—
316C8×Q8—471no—
317C8×Q8—471no—
318C8×Q8C2×D4711yescharacteristic
319C4×Q16—471no—
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16—471no—
323C4×SD16—471no—
324C4×SD16C2×D4711yescharacteristic
325C4×D8—471no—
326C4×D8—471no—
327C8×D4—471no—
328C8×D4—471no—
329C8×D4—471no—
330C8×D4—941no—
331C8×D4—941no—
332C8×D4—941no—
333C8×D4—941no—
334C8×D4C2×D4711yescharacteristic
335#431—471no—
336#431—471no—
337#431—941no—
338#431—941no—
339#427—471no—
340C2×C4⋊C8—471no—
341C2×C4⋊C8—471no—
342C2×C4⋊C8—941no—
343C2×C4⋊C8—941no—
344#416—471no—
345#416—471no—
346C2×C4×C8—471no—
347#335—471no—
348#335—471no—
349#335—471no—
350#335C2×D4711yescharacteristic
351Q8⋊C8—471no—
352Q8⋊C8—471no—
353Q8⋊C8—471no—
354Q8⋊C8C2×D4711yescharacteristic
355D4⋊C8—471no—
356D4⋊C8—471no—
357D4⋊C8—471no—
358D4⋊C8C2×D4711yescharacteristic
359#322—471no—
360#322C2×D4711yescharacteristic
361C82—471no—
362C82—471no—
363C47#1785711yescharacteristic, complemented, Sylow
364C2×#41—471no—
365C2×#41—471no—
366#135—478no—
367C2×Q16—471no—
368C2×SD16—471no—
369C2×SD16C4×D4711yescharacteristic
370C2×D8—471no—
371C22×C8—21no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—941no—
375C22×C8—941no—
376C22×C8—941no—
377C22×C8—941no—
378C22×C8—941no—
379C4×Q8—471no—
380C4×Q8—471no—
381C4×Q8—471no—
382C4×Q8C22×D4711yescharacteristic
383C4×D4—471no—
384C4×D4—471no—
385C4×D4—471no—
386C4×D4—941no—
387C4×D4—941no—
388C4×D4—941no—
389C4×D4—941no—
390C4×D4C22×D4711yescharacteristic
391#117—471no—
392#117—471no—
393#117—941no—
394#117—941no—
395C2×C42—471no—
396C2×C42—941no—
397C2×C42—941no—
398#107—471no—
399#107—471no—
400#106—471no—
401#106C4×D4711yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—471no—
404C4⋊C8—471no—
405C4⋊C8—471no—
406C4⋊C8—471no—
407C4⋊C8—941no—
408C4⋊C8—941no—
409C4⋊C8—941no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8C22×D4711yescharacteristic
414C4⋊C8C22×D4711yescharacteristic
415#103—471no—
416#103—471no—
417#103—471no—
418#103C4×D4711yescharacteristic
419#102—471no—
420#102—471no—
421#102—471no—
422#102C4×D4711yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—471no—
425C22⋊C8—471no—
426C22⋊C8—941no—
427C22⋊C8—941no—
428C22⋊C8—941no—
429C22⋊C8—941no—
430C4×C8—21no—
431C4×C8—471no—
432C4×C8—471no—
433C4×C8—471no—
434C4×C8—471no—
435C4×C8—471no—
436C4×C8—941no—
437C4×C8—941no—
438C4×C8—941no—
439C4×C8C22×D4711yescharacteristic
440C4×C8C22×D4711yescharacteristic
441C4×C8C22×D4711yescharacteristic
442#41—474no—
443#41—474no—
444#41—942no—
445#41—942no—
446C2×Q8—471no—
447C2×Q8C2×C4×D4711yescharacteristic
448C2×D4—471no—
449C2×D4—941no—
450C2×D4—941no—
451C2×D4C2×C4×D4711yescharacteristic
452C22×C4—21no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—471no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461Q16—474no—
462SD16—474no—
463SD16C8×D4714yescomplemented
464D8—474no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—81no—
469C2×C8—471no—
470C2×C8—474no—
471C2×C8—471no—
472C2×C8—471no—
473C2×C8—471no—
474C2×C8—942no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—3761no—
479C2×C8—3761no—
480C2×C8—3761no—
481C2×C8—3761no—
482C2×C8—3761no—
483C2×C8C2×C4×D4711yescharacteristic
484C2×C8C2×C4×D4711yescharacteristic
485C2×C8D4×D4711yescharacteristic
486C2×C8D4×D4711yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—471no—
489C4⋊C4—471no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4C2×C4×D4711yescharacteristic
494C4⋊C4C2×C4×D4711yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—941no—
497C22⋊C4—941no—
498C22⋊C4—941no—
499C22⋊C4—941no—
500C22⋊C4—941no—
501C42—21no—
502C42—471no—
503C42—471no—
504C42—471no—
505C42—941no—
506C42—941no—
507C42—941no—
508C42—941no—
509C42—941no—
510C42C23×D4711yescharacteristic
511C23—21no—
512C23—471no—
513C23—941no—
514Q8—21no—
515Q8—472no—
516Q8—941no—
517Q8C2×C8×D4712yes—
518D4—21no—
519D4—472no—
520D4—944no—
521D4—944no—
522D4—941no—
523D4C2×C8×D4712yes—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—471no—
530C2×C4—472no—
531C2×C4—472no—
532C2×C4—471no—
533C2×C4—471no—
534C2×C4—944no—
535C2×C4—944no—
536C2×C4—941no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—3761no—
542C2×C4—3761no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4C22×C4×D4711yescharacteristic
547C2×C4C2×D4×D4711yescharacteristic
548C2×C4#41×D4711yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—472no—
556C8—941no—
557C8—941no—
558C8—941no—
559C8—1881no—
560C8—1881no—
561C8—1881no—
562C8C2×C8×D4712yes—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—472no—
567C22—941no—
568C22—941no—
569C22—942no—
570C22—1881no—
571C22—1881no—
572C22C4×D4×D4711yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—472no—
578C4—941no—
579C4—941no—
580C4—942no—
581C4—1881no—
582C4—1881no—
583C4C22×C8×D4711yescharacteristic
584C4#131×D4711yescharacteristic
585C4#1568992711yescharacteristic
586C4#1568993911yescharacteristic
587C2—42no—
588C2—942no—
589C2—1882no—
590C2C8×D4×D4711yescharacteristic
591C2#2025226011yescharacteristic
592C2#2025230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC47×SD16⋊C8C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094045C4
cosocleC42×C47C24
hypercenterSD16⋊C8D47
hypocenterC47#17857
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
1. #20252498C2semidirect
2. #20252495C2semidirect
4. #20242202C2semidirect
5. SD16⋊(C47⋊C8)C2semidirect
6. #20242199C2semidirect
7. C8×#10625337C2semidirect
8. #20242192C2semidirect
9. C8×#10625334C2semidirect
10. #20242180C2semidirect
11. #335×D47C2semidirect
12. #20241774C2semidirect
13. #20241772C2semidirect
14. #20241673C2semidirect
15. C47×SD16⋊C8C2semidirect
69. #13094045C8semidirect
152. #10625354C2×C8semidirect
154. #10625352C2×C8semidirect
164. SD16×C47C2×C8semidirect
180. #10625337C2×C8semidirect
181. #10625334C2×C8semidirect
207. #10625325C2×C8semidirect
213. C8×D47C2×C8semidirect
297. SD16⋊C8D47semidirect
363. C47#17857semidirect
463. SD16C8×D47semidirect

Maximal subgroups

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

subgroupindex
#202524982
#202524952
C4×#130940452
#202422022
SD16⋊(C47⋊C8)2
#202421992
C8×#106253372
#202421922
C8×#106253342
#202421802
#335×D472
#202417742
#202417722
#202416732
C47×SD16⋊C82
#1785747