Finite Group Databasebeta

← #26233639

Subgroups — #26233639

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689117C211yesmaximal, characteristic
2#20251834C211yesmaximal, characteristic
3#20244091C212yesmaximal, complemented
4#20244036C212yesmaximal, complemented
5#20243662C212yesmaximal, complemented
6#20243487C211yesmaximal, characteristic, complemented
7#20243424C211yesmaximal, characteristic, complemented
8#20243331C211yesmaximal, characteristic
9#20243227C212yesmaximal, complemented
10#20243162C211yesmaximal, characteristic, complemented
11C47×#2924C211yesmaximal, characteristic, complemented
12C22×#10625350C2211yescharacteristic
13C2×#13094030C2212yes—
14C23×C47⋊C8C2211yescharacteristic
15C2×#13093959C2212yescomplemented
16C2×#13093950C2212yes—
17C2×#13093950C2212yes—
18#15689117C411yescharacteristic, complemented
19#15689117C411yescharacteristic, complemented
20#15689117C411yescharacteristic, complemented
21#15689117C411yescharacteristic, complemented
22#15689117C2211yescharacteristic
23#15689117C2211yescharacteristic
24#15689117C2211yescharacteristic
25#15689117C2211yescharacteristic
26C2×#13093947C411yescharacteristic, complemented
27C2×#13093947C411yescharacteristic, complemented
28C2×#13093944C411yescharacteristic, complemented
29C2×#13093944C411yescharacteristic, complemented
30#15689089C2212yes—
31#15689088—22no—
32#15689087C2211yescharacteristic
33#15689085—21no—
34C22⋊C8×D47—21no—
35C2×C8×Dic47C2212yescomplemented
36C4×C22⋊Dic47C2211yescharacteristic
37#15688887C2212yescomplemented
38#15688882C2212yescomplemented
39#15688882C2212yescomplemented
40#15688877C2212yescomplemented
41C2×#117×C47C2211yescharacteristic
42C47×#433—22no—
43C47×#432—21no—
44C47×#431—21no—
45C47×#424C2212yescomplemented
46C47×#407C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#405C2212yescomplemented
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—24no—
52C2×#10625350—42no—
53C2×#10625350C2×C411yescharacteristic
54C2×#10625350C2×C411yescharacteristic
55C2×#10625350C2311yescharacteristic
56C2×#10625350C2311yescharacteristic
57C22×Dic94C2×C411yescharacteristic
58C22×D188C2×C411yescharacteristic
59C22×C22⋊D47—21no—
60C22×C4×D47—21no—
61#13094030—24no—
62#13094030—42no—
63C2×#10625329C2312yes—
64C2×#10625324—22no—
65C22×C47⋊C8—42no—
66C22×C47⋊C8C2×C411yescharacteristic
67C22×C47⋊C8C2×C411yescharacteristic
68C22×C47⋊C8C2×C411yescharacteristic
69C22×C47⋊C8C2×C411yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C2×C8×D47—22no—
73C2×C22⋊Dic47—21no—
74C2×C4×Dic47C2312yes—
75#13093959—42no—
76#13093950—24no—
77#13093950—42no—
78#13093947C2×C411yescharacteristic
79#13093947C2×C411yescharacteristic
80#13093947C2×C411yescharacteristic
81#13093947C2×C411yescharacteristic
82#13093947C2×C411yescharacteristic
83#13093947C2×C411yescharacteristic
84#13093947C2×C411yescharacteristic
85#13093947C2×C411yescharacteristic
86#13093944C2×C411yescharacteristic
87#13093944C2×C411yescharacteristic
88#13093944C2×C411yescharacteristic
89#13093944C2×C411yescharacteristic
90#13093944C2×C411yescharacteristic
91#13093944C2×C411yescharacteristic
92#13093944C2×C411yescharacteristic
93#13093944C2×C411yescharacteristic
94C22⋊(C47⋊C8)—21no—
95C22⋊(C47⋊C8)—21no—
96(C2×D47)⋊C8—22no—
97(C2×D47)⋊C8—22no—
98C8×Dic47—42no—
99C47⋊#95—21no—
100C23×C4×C47C2311yescharacteristic
101C2×M16×C47C2312yes—
102C22×C8×C47C2312yes—
103#117×C47—21no—
104#117×C47—21no—
105#117×C47C2×C411yescharacteristic
106#117×C47C2×C411yescharacteristic
107#117×C47C2311yescharacteristic
108#117×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2×C411yescharacteristic
110C2×C4⋊C4×C47C2×C411yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C42×C47—21no—
113C4⋊C8×C47—22no—
114C4⋊C8×C47—22no—
115C22⋊C8×C47—21no—
116C22⋊C8×C47—21no—
117C22⋊C8×C47D411yescharacteristic
118C22⋊C8×C47D411yescharacteristic
119C22⋊C8×C47D412yes—
120#97×C47—22no—
121C4×C8×C47—22no—
122C24×C47#4111yescharacteristic
123C23×D47—21no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47C2411yescharacteristic
134C2×C22⋊D47—21no—
135C2×C22⋊D47—21no—
136C2×C22⋊D47—21no—
137C2×C22⋊D47—21no—
138C2×C22⋊D47—44no—
139C22×Dic47—21no—
140C22×Dic47—22no—
141#10625350—22no—
142#10625350—22no—
143#10625350—22no—
144#10625350—22no—
145#10625350—22no—
146#10625350—41no—
147#10625350—41no—
148#10625350—44no—
149#10625350—44no—
150#10625350#4114yes—
151C2×D188—22no—
152C2×D188—21no—
153C2×D188—41no—
154C2×D188C22×C411yescharacteristic
155C2×D188C22×C411yescharacteristic
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—44no—
161C2×Dic94—22no—
162C2×Dic94—21no—
163C2×Dic94—41no—
164C2×Dic94C22×C411yescharacteristic
165C2×Dic94C22×C411yescharacteristic
166M16×C47—22no—
167M16×C47—22no—
168C2×C8×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47C2×D412yes—
172C2×C8×C47C2×D412yes—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47C22×C411yescharacteristic
176C4⋊C4×C47C22×C411yescharacteristic
177C4⋊C4×C47C22×C411yescharacteristic
178C4⋊C4×C47C22×C411yescharacteristic
179C22⋊C4×C47—21no—
180C22⋊C4×C47—21no—
181C22⋊C4×C47—21no—
182C22⋊C4×C47—21no—
183C42×C47—21no—
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C22⋊Dic47—24no—
188C4×Dic47—22no—
189C4×Dic47—22no—
190#10625329—22no—
191#10625329—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C2×C47⋊C8—41no—
198C2×C47⋊C8—41no—
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203#10625324—44no—
204C8×D47—44no—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—41no—
208C23×C47C4×D411yescharacteristic
209C23×C47C4×D411yescharacteristic
210C23×C47C2×#4111yescharacteristic
211C22×D47—21no—
212C22×D47—21no—
213C22×D47—42no—
214C22×D47—42no—
215C22×D47—81no—
216C2×C4×C47—22no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—42no—
228C2×C4×C47—81no—
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C2×#4112yes—
234C2×C4×C47H(5,𝔽2)12yes—
235C22⋊D47—24no—
236C22⋊D47—42no—
237C22⋊D47—42no—
238C22⋊D47—42no—
239C2×Dic47—21no—
240C2×Dic47—24no—
241C2×Dic47—21no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245D188—21no—
246D188—21no—
247D188—21no—
248D188—42no—
249D188#11712yes—
250C4×D47—24no—
251C4×D47—42no—
252C4×D47—42no—
253C4×D47—42no—
254Dic94—21no—
255Dic94—21no—
256Dic94—21no—
257Dic94—42no—
258Dic94#11712yes—
259C8×C47—22no—
260C8×C47—22no—
261C8×C47—42no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—42no—
267#22587—471nomaximal, Sylow
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—44no—
276C22×C47#44312yes—
277C22×C47C2×C4×D411yescharacteristic
278C22×C47#55112yes—
279C2×D47—22no—
280C2×D47—41no—
281C2×D47—41no—
282C2×D47—41no—
283C2×D47—41no—
284C2×D47—41no—
285C2×D47—84no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47C2×#11711yescharacteristic
293C4×C47#51811yescharacteristic
294C4×C47#54612yes—
295Dic47—22no—
296Dic47—44no—
297Dic47—41no—
298#2924D4711yescharacteristic, complemented
299C2×#416—471no—
300#2880—471no—
301#1937—472no—
302#1929—472no—
303#1866—472no—
304#1826—471no—
305#1810—471no—
306#1789—471no—
307#1764—472no—
308C8×C22⋊C4—471no—
309C2×C47—22no—
310C2×C47—22no—
311C2×C47—41no—
312C2×C47#234211yescharacteristic
313C2×C47C2×#44311yescharacteristic
314C2×C47#295711yescharacteristic
315D47—42no—
316D47—81no—
317C22×#41—471no—
318C2×#131—472no—
319C23×C8—471no—
320C2×#117C2×D4711yescharacteristic
321#433—22no—
322#432—21no—
323#431—21no—
324C2×#108—472no—
325#424C2×D4712yescomplemented
326C2×#104—472no—
327C2×#104—472no—
328#416—471no—
329#416—471no—
330#416—471no—
331#416—471no—
332#416—471no—
333#416—471no—
334#416—471no—
335#416—471no—
336C2×#103—471no—
337C2×#103—471no—
338C2×#102—471no—
339C2×#102—471no—
340#408—472no—
341#408—942no—
342#407—471no—
343#407—941no—
344#407C2×D4711yescharacteristic
345C2×C22⋊C8—941no—
346C2×C22⋊C8C2×D4711yescharacteristic
347#405C2×D4712yescomplemented
348C2×C4×C8—472no—
349C4×C22⋊C4—471no—
350#341—472no—
351#339—472no—
352#339—472no—
353#336—472no—
354C47#2258711yescharacteristic, complemented, Sylow
355C2×#41—471no—
356C2×#41—471no—
357C2×#41—471no—
358C2×#41—471no—
359C2×#41—944no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—1882no—
363C22×Q8—471no—
364C22×D4—471no—
365C22×D4—941no—
366C23×C4—941no—
367C23×C4C22×D4711yescharacteristic
368#131—944no—
369#131—1882no—
370C2×M16—472no—
371C2×M16—942no—
372C2×M16C22×D4712yes—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—471no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8—942no—
380C22×C8—1882no—
381C22×C8C22×D4712yes—
382#117—21no—
383#117—21no—
384#117C4×D4711yescharacteristic
385#117C4×D4711yescharacteristic
386#117C22×D4711yescharacteristic
387#117C22×D4711yescharacteristic
388C2×C4⋊C4C4×D4711yescharacteristic
389C2×C4⋊C4C4×D4711yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—941no—
392C2×C42—21no—
393C2×C42—472no—
394#108—1882no—
395C4⋊C8—22no—
396C4⋊C8—22no—
397#104—944no—
398#104—1882no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#103—471no—
405#103—471no—
406#103—471no—
407#102—471no—
408#102—471no—
409#102—471no—
410#102—471no—
411#102—471no—
412#102—471no—
413#102—471no—
414#102—471no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—942no—
420C22⋊C8—942no—
421C22⋊C8C22⋊D4711yescharacteristic
422C22⋊C8C22⋊D4711yescharacteristic
423C22⋊C8C22⋊D4712yes—
424#97—22no—
425C4×C8—22no—
426C4×C8—1882no—
427#95—941no—
428C24—941no—
429C24#1062535011yescharacteristic
430#41—474no—
431#41—942no—
432#41—942no—
433#41—942no—
434#41—942no—
435#41—942no—
436#41—1884no—
437#41—1881no—
438#41—1881no—
439#41—1884no—
440C2×Q8—471no—
441C2×Q8—471no—
442C2×Q8—942no—
443C2×Q8—941no—
444C2×Q8—1881no—
445C2×D4—471no—
446C2×D4—471no—
447C2×D4—942no—
448C2×D4—941no—
449C2×D4—941no—
450C2×D4—941no—
451C2×D4—941no—
452C2×D4—941no—
453C2×D4—1881no—
454C2×D4—1884no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—942no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4—1884no—
466C22×C4C2×C4×D4711yescharacteristic
467C22×C4C2×C4×D4711yescharacteristic
468C22×C4#1062535011yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471C22×C4C23×D4711yescharacteristic
472M16—22no—
473M16—22no—
474M16—942no—
475M16—942no—
476M16—1884no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—471no—
481C2×C8—471no—
482C2×C8—471no—
483C2×C8—471no—
484C2×C8—942no—
485C2×C8—942no—
486C2×C8—942no—
487C2×C8—1884no—
488C2×C8—1881no—
489C2×C8—1881no—
490C2×C8—1881no—
491C2×C8—1881no—
492C2×C8C2×C22⋊D4712yes—
493C2×C8C2×C22⋊D4712yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C2×C4×D4711yescharacteristic
497C4⋊C4C2×C4×D4711yescharacteristic
498C4⋊C4C2×C4×D4711yescharacteristic
499C4⋊C4C2×C4×D4711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—944no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—942no—
510C42—942no—
511C23—22no—
512C23—22no—
513C23—41no—
514C23—941no—
515C23—941no—
516C23—3761no—
517C23—1882no—
518C23—1882no—
519C23C4×C22⋊D4711yescharacteristic
520C23C4×C22⋊D4711yescharacteristic
521C23C2×#1062535011yescharacteristic
522Q8—472no—
523Q8—941no—
524Q8—941no—
525Q8—941no—
526Q8—1882no—
527D4—472no—
528D4—944no—
529D4—941no—
530D4—941no—
531D4—941no—
532D4—1882no—
533D4—1882no—
534D4—1882no—
535D4—1882no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—42no—
548C2×C4—81no—
549C2×C4—941no—
550C2×C4—944no—
551C2×C4—944no—
552C2×C4—941no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4C4×C22⋊D4711yescharacteristic
560C2×C4C4×C22⋊D4711yescharacteristic
561C2×C4C22×C4×D4711yescharacteristic
562C2×C4C22×C22⋊D4711yescharacteristic
563C2×C4#41×D4712yes—
564C2×C4#1309407012yes—
565C8—22no—
566C8—22no—
567C8—42no—
568C8—941no—
569C8—941no—
570C8—941no—
571C8—941no—
572C8—1882no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—44no—
581C22—942no—
582C22—3764no—
583C22—1881no—
584C22—1881no—
585C22—1881no—
586C22—1881no—
587C22—1881no—
588C22#1568923812yes—
589C22C2×C4×C22⋊D4711yescharacteristic
590C22#1568979712yes—
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—942no—
598C4—1884no—
599C4—1881no—
600C4#117×D4711yescharacteristic
601C4#1568959711yescharacteristic
602C4#1568976112yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—3761no—
607C2—1882no—
608C2#2024623811yescharacteristic
609C2C2×#1568923811yescharacteristic
610C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2924C2
socleC22×C47C2×C4×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#2924D47
hypocenterC47#22587
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #20244091C2semidirect
4. #20244036C2semidirect
5. #20243662C2semidirect
6. #20243487C2semidirect
7. #20243424C2semidirect
9. #20243227C2semidirect
10. #20243162C2semidirect
11. C47×#2924C2semidirect
15. C2×#13093959C22semidirect
18. #15689117C4semidirect
19. #15689117C4semidirect
20. #15689117C4semidirect
21. #15689117C4semidirect
26. C2×#13093947C4semidirect
27. C2×#13093947C4semidirect
28. C2×#13093944C4semidirect
29. C2×#13093944C4semidirect
35. C2×C8×Dic47C22semidirect
37. #15688887C22semidirect
38. #15688882C22semidirect
39. #15688882C22semidirect
40. #15688877C22semidirect
45. C47×#424C22semidirect
48. C47×#405C22semidirect
298. #2924D47semidirect
325. #424C2×D47semidirect
347. #405C2×D47semidirect
354. C47#22587semidirect

Maximal subgroups

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

subgroupindex
C2×#156891172
#202518342
#202440912
#202440362
#202436622
#202434872
#202434242
#202433312
#202432272
#202431622
C47×#29242
#2258747