Finite Group Databasebeta

← #26187395

Subgroups — #26187395

Order 12032.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253442C211yesmaximal, characteristic
2#20252405C211yesmaximal, characteristic, complemented
3#20252132C211yesmaximal, characteristic, complemented
4#20242299C211yesmaximal, characteristic, complemented
5#20242270C211yesmaximal, characteristic, complemented
6#20242269C211yesmaximal, characteristic, complemented
7#20242249C211yesmaximal, characteristic, complemented
8#20242234C211yesmaximal, characteristic, complemented
9#20242214C211yesmaximal, characteristic, complemented
10#20242197C211yesmaximal, characteristic, complemented
11#20242191C211yesmaximal, characteristic, complemented
12#20242174C211yesmaximal, characteristic, complemented
13#20241776C211yesmaximal, characteristic, complemented
14#20241683C211yesmaximal, characteristic, complemented
15C47×#1496C211yesmaximal, characteristic, complemented
16C2×#13094031—21no—
17C4×#10625350C2211yescharacteristic
18#15689444C411yescharacteristic
19#15689444C411yescharacteristic
20#15689415C411yescharacteristic
21#15689410C411yescharacteristic
22#15689320C411yescharacteristic
23#15689315C411yescharacteristic
24#15689266C411yescharacteristic
25#15689266C411yescharacteristic
26#15689247C2211yescharacteristic
27#15689247C2211yescharacteristic
28C4×#10625335C2211yescharacteristic
29C4×#10625335C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31C4×#10625334C2211yescharacteristic
32#15689201C2211yescharacteristic
33#15689201C2211yescharacteristic
34#15689200C2211yescharacteristic
35#15689200C2211yescharacteristic
36#15689198—21no—
37#15689198—21no—
38#15689195—21no—
39#15689195—21no—
40D4×C47⋊C8C2211yescharacteristic
41D4×C47⋊C8C2211yescharacteristic
42#15689178—21no—
43#15689176C2211yescharacteristic
44C2×C4⋊(C47⋊C8)C2211yescharacteristic
45#15689090—21no—
46C4×#10625329C2211yescharacteristic
47#15689075—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#532C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72#13094031—44no—
73C2×#10625329—21no—
74C2×#10625329—21no—
75C2×#10625329D411yescharacteristic
76C2×#10625329D411yescharacteristic
77C2×#10625324—21no—
78C2×#10625324—21no—
79C22×C47⋊C8—21no—
80C22×C47⋊C8—21no—
81C22×C47⋊C8—21no—
82C4×Dic94C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×D188C2×C411yescharacteristic
85C4×D188C2311yescharacteristic
86C4×C22⋊D47—21no—
87C4×C22⋊D47—21no—
88#13093983C2×C411yescharacteristic
89#13093981—21no—
90C42×D47—21no—
91#13093957C2×C411yescharacteristic
92#13093957C2×C411yescharacteristic
93#13093955C2×C411yescharacteristic
94#13093955C2×C411yescharacteristic
95C4⋊(C47⋊C8)—21no—
96C4⋊(C47⋊C8)C2×C411yescharacteristic
97C4⋊(C47⋊C8)C2×C411yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102#13093947C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093945C2×C411yescharacteristic
106#13093945C2×C411yescharacteristic
107#13093945C2×C411yescharacteristic
108#13093944C2×C411yescharacteristic
109#13093944C2×C411yescharacteristic
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)—21no—
113C22⋊(C47⋊C8)—21no—
114C22⋊(C47⋊C8)C2×C411yescharacteristic
115C22⋊(C47⋊C8)C2×C411yescharacteristic
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118#13093935D411yescharacteristic
119#13093935D411yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C8×Dic47—21no—
126C2×#41×C47—21no—
127C4⋊Q8×C47C2×C411yescharacteristic
128#127×C47C2×C411yescharacteristic
129#124×C47—21no—
130#121×C47—21no—
131#121×C47C2×C411yescharacteristic
132#121×C47C2×C411yescharacteristic
133C4×D4×C47—21no—
134C4×D4×C47C2311yescharacteristic
135C4×D4×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47—21no—
138C4⋊C8×C47C2311yescharacteristic
139C4⋊C8×C47C2311yescharacteristic
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142#97×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145#41×C47—42no—
146#41×C47—42no—
147C2×Q8×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47C22×C411yescharacteristic
153C2×D4×C47C22×C411yescharacteristic
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47#4111yescharacteristic
159C2×C22⋊D47—21no—
160#10625350—22no—
161#10625350—41no—
162C2×D188C22×C411yescharacteristic
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—21no—
166C2×Dic94C22×C411yescharacteristic
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47C22×C411yescharacteristic
173C4⋊C4×C47C22×C411yescharacteristic
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C42×C47C22×C411yescharacteristic
179C42×C47C2×D411yescharacteristic
180C42×C47#4111yescharacteristic
181C42×C47C2411yescharacteristic
182C22⋊Dic47—21no—
183#10625335—22no—
184#10625335—22no—
185#10625334—41no—
186#10625334—41no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189C4⋊Dic47C22×C411yescharacteristic
190C4⋊Dic47C22×C411yescharacteristic
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196#10625329—22no—
197#10625329—41no—
198#10625329—42no—
199#10625329—42no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—42no—
203C2×C47⋊C8—42no—
204C2×C47⋊C8—42no—
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C22×C411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210C2×C47⋊C8C2×D411yescharacteristic
211C2×C47⋊C8C2×D411yescharacteristic
212C2×C47⋊C8C2×D411yescharacteristic
213#10625324—42no—
214#10625324—42no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47C4×D411yescharacteristic
218C22×D47—21no—
219Q8×C47—42no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—42no—
225D4×C47—42no—
226D4×C47—42no—
227D4×C47—81no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C22⋊D47—42no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249D188—21no—
250D188—21no—
251C4×D47—42no—
252C4×D47—41no—
253C4×D47—41no—
254C4×D47—81no—
255Dic94—21no—
256Dic94#13112yescomplemented
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—21no—
267C47⋊C8—21no—
268C47⋊C8—41no—
269C47⋊C8—41no—
270C47⋊C8AGL(1,ℤ/8)12yes—
271#18011—471nomaximal, Sylow
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47C2×C4×D411yescharacteristic
282C2×D47—41no—
283C2×D47—41no—
284C2×D47—41no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—21no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47C2×#13111yescharacteristic
292C4×C47#56811yescharacteristic
293C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C47#57511yescharacteristic
295Dic47—22no—
296Dic47—41no—
297Dic47—41no—
298#3106—471no—
299#2971—471no—
300#2935—471no—
301#1594—471no—
302#1589—471no—
303#1588—471no—
304#1586—471no—
305#1583—471no—
306#1581—471no—
307SD16⋊C8—471no—
308C8×SD16—471no—
309#1573—471no—
310#1496D4711yescharacteristic, complemented
311#1477—471no—
312#1453—471no—
313C2×C47—41no—
314C2×C47—81no—
315C2×C47—81no—
316C2×C47#293311yescharacteristic
317C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C47#295711yescharacteristic
319D47—81no—
320C2×#131—941no—
321#532C2×D4711yescharacteristic
322C4×#41—471no—
323#482—471no—
324#482—471no—
325#477—471no—
326#476—471no—
327#460—471no—
328#459—471no—
329#449—471no—
330#449—471no—
331C8×Q8—471no—
332C8×Q8—471no—
333C4×SD16—471no—
334C4×SD16—471no—
335C4×D8—471no—
336C4×D8—471no—
337#436—471no—
338#436—471no—
339#436—471no—
340#436—471no—
341#436—941no—
342#436—941no—
343#435—941no—
344#435—941no—
345C8×D4—471no—
346C8×D4—471no—
347#432—941no—
348#432C2×D4711yescharacteristic
349#431—471no—
350#431C2×D4711yescharacteristic
351C2×C4⋊C8—471no—
352#408—941no—
353C4×M16—471no—
354C4×M16—941no—
355#335—471no—
356#335—471no—
357#334—471no—
358#334—471no—
359Q8⋊C8—471no—
360Q8⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8C2×D4711yescharacteristic
364D4⋊C8C2×D4711yescharacteristic
365D4⋊C8C2×D4711yescharacteristic
366D4⋊C8C2×D4711yescharacteristic
367#322—471no—
368#322—471no—
369#322—471no—
370C82—471no—
371C47#1801111yescharacteristic, complemented, Sylow
372C2×#41—21no—
373C2×#41—471no—
374C2×SD16—471no—
375C2×SD16—471no—
376C2×D8—471no—
377C2×D8—471no—
378#131—1884no—
379C2×M16—471no—
380C2×M16—471no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C22×C8—941no—
386C22×C8—941no—
387C22×C8—941no—
388C4⋊Q8C4×D4711yescharacteristic
389#127C4×D4711yescharacteristic
390#124—21no—
391#121—21no—
392#121C4×D4711yescharacteristic
393#121C4×D4711yescharacteristic
394C4×Q8—471no—
395C4×Q8—471no—
396C4×D4—21no—
397C4×D4—471no—
398C4×D4—471no—
399C4×D4—941no—
400C4×D4—941no—
401C4×D4C22×D4711yescharacteristic
402C4×D4C22×D4711yescharacteristic
403#117—471no—
404#117—941no—
405C2×C42—941no—
406C2×C42C22×D4711yescharacteristic
407#107—471no—
408#107—471no—
409#106—471no—
410#106—471no—
411C4⋊C8—21no—
412C4⋊C8—471no—
413C4⋊C8—471no—
414C4⋊C8—471no—
415C4⋊C8—471no—
416C4⋊C8—941no—
417C4⋊C8—941no—
418C4⋊C8—941no—
419C4⋊C8C22×D4711yescharacteristic
420C4⋊C8C22×D4711yescharacteristic
421#103—471no—
422#103—471no—
423#102—471no—
424#102—471no—
425#102—471no—
426#102—471no—
427#102—471no—
428#102—471no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—471no—
432C22⋊C8—471no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437C22⋊C8—941no—
438C22⋊C8—941no—
439#97—21no—
440#97—471no—
441#97—471no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—471no—
445C4×C8—471no—
446C4×C8—941no—
447C4×C8—941no—
448C4×C8C22×D4711yescharacteristic
449C4×C8C22×D4711yescharacteristic
450#41—42no—
451#41—42no—
452#41—942no—
453#41—1881no—
454C2×Q8—21no—
455C2×Q8—471no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—471no—
461C2×D4—941no—
462C2×D4C2×C4×D4711yescharacteristic
463C2×D4C2×C4×D4711yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—941no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4C2×C4×D4711yescharacteristic
470C22×C4D4×D4711yescharacteristic
471C22×C4#1062535211yescharacteristic
472SD16—942no—
473SD16—942no—
474D8—1881no—
475D8—1881no—
476M16—942no—
477M16—1882no—
478M16—1882no—
479M16—1882no—
480M16—1881no—
481M16—1882no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—471no—
487C2×C8—471no—
488C2×C8—471no—
489C2×C8—471no—
490C2×C8—471no—
491C2×C8—471no—
492C2×C8—471no—
493C2×C8—471no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—1882no—
497C2×C8—1882no—
498C2×C8—1882no—
499C4⋊C4—21no—
500C4⋊C4—471no—
501C4⋊C4—471no—
502C4⋊C4—941no—
503C4⋊C4—941no—
504C4⋊C4C2×C4×D4711yescharacteristic
505C4⋊C4C2×C4×D4711yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—941no—
511C22⋊C4—941no—
512C22⋊C4—941no—
513C42—941no—
514C42—941no—
515C42—941no—
516C42C2×C4×D4711yescharacteristic
517C42D4×D4711yescharacteristic
518C42#1062535211yescharacteristic
519C42C23×D4711yescharacteristic
520C23—21no—
521C23—21no—
522C23—941no—
523C23(C22⋊D47)⋊C411yescharacteristic
524Q8—42no—
525Q8—472no—
526Q8—941no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—941no—
536D4—941no—
537D4—1882no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—3761no—
553C2×C4—1882no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4(C22⋊D47)⋊C411yescharacteristic
557C2×C4(C22⋊D47)⋊C411yescharacteristic
558C2×C4(C22⋊D47)⋊C411yescharacteristic
559C2×C4C22×C4×D4711yescharacteristic
560C2×C4C2×D4×D4711yescharacteristic
561C2×C4C2×#1062535211yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—472no—
567C8—941no—
568C8—941no—
569C8—941no—
570C8—941no—
571C8—941no—
572C8—941no—
573C8—941no—
574C8—1881no—
575C8—1881no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—1881no—
586C22—1881no—
587C22—1881no—
588C22C2×(C22⋊D47)⋊C411yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—942no—
596C4—1881no—
597C4—1881no—
598C4#131×D4711yescharacteristic
599C4#1568988811yescharacteristic
600C4AGL(1,ℤ/8)×D4711yescharacteristic
601C4#1568991911yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—3761no—
606C2#2025211811yescharacteristic
607C2#2025219211yescharacteristic
608C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1496C2
socleC22×C47C2×C4×D4
prime radical#20253442C2
cosocleC42×C47C24
hypercenter#1496D47
hypocenterC47#18011
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #20252405C2semidirect
3. #20252132C2semidirect
4. #20242299C2semidirect
5. #20242270C2semidirect
6. #20242269C2semidirect
7. #20242249C2semidirect
8. #20242234C2semidirect
9. #20242214C2semidirect
10. #20242197C2semidirect
11. #20242191C2semidirect
12. #20242174C2semidirect
13. #20241776C2semidirect
14. #20241683C2semidirect
15. C47×#1496C2semidirect
256. Dic94#131semidirect
310. #1496D47semidirect
371. C47#18011semidirect

Maximal subgroups

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

subgroupindex
#202534422
#202524052
#202521322
#202422992
#202422702
#202422692
#202422492
#202422342
#202422142
#202421972
#202421912
#202421742
#202417762
#202416832
C47×#14962
#1801147