Finite Group Databasebeta

← #26186902

Subgroups — #26186902

Order 12032.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253977C211yesmaximal, characteristic
2#20252533C211yesmaximal, characteristic, complemented
3#20252464C211yesmaximal, characteristic, complemented
4#20242299C211yesmaximal, characteristic, complemented
5#20242287C211yesmaximal, characteristic, complemented
6#20242281C211yesmaximal, characteristic, complemented
7#20242270C211yesmaximal, characteristic, complemented
8#20242209C211yesmaximal, characteristic, complemented
9#20242197C211yesmaximal, characteristic, complemented
10#20242191C211yesmaximal, characteristic, complemented
11#20242180C211yesmaximal, characteristic, complemented
12#20242153C211yesmaximal, characteristic, complemented
13#20241849C211yesmaximal, characteristic, complemented
14C8×#10625329C211yesmaximal, characteristic, complemented
15C47×#1492C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689529C411yescharacteristic
18#15689510C411yescharacteristic
19#15689487C411yescharacteristic
20#15689485C411yescharacteristic
21#15689374C411yescharacteristic
22#15689374C411yescharacteristic
23#15689367C411yescharacteristic
24#15689367C411yescharacteristic
25#15689250C2211yescharacteristic
26#15689247C2211yescharacteristic
27C4×#10625335C2211yescharacteristic
28C4×#10625335C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689201C2211yescharacteristic
32#15689201C2211yescharacteristic
33#15689200C2211yescharacteristic
34#15689199—21no—
35#15689195—21no—
36#15689195—21no—
37#15689192—21no—
38D4×C47⋊C8C2211yescharacteristic
39D4×C47⋊C8C2211yescharacteristic
40#15689188C2211yescharacteristic
41#15689183—21no—
42#15689180C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689148—21no—
45#15689090—21no—
46#15689090—21no—
47C4×#10625329C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#532C2211yescharacteristic
61C47×#423C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625335C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625334C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329C2×C411yescharacteristic
74C2×#10625329C2×C411yescharacteristic
75C2×#10625324—21no—
76C22×C47⋊C8—21no—
77C22×C47⋊C8—21no—
78C2×C8×D47—21no—
79#13094018—21no—
80#13094016C2×C411yescharacteristic
81#13094012C2×C411yescharacteristic
82#13094007—21no—
83#13094003C2×C411yescharacteristic
84#13093998C2×C411yescharacteristic
85C4×Dic94C2311yescharacteristic
86C4×D188C2311yescharacteristic
87C4×C22⋊D47—21no—
88#13093981—21no—
89#13093957C2×C411yescharacteristic
90#13093957C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92#13093955C2×C411yescharacteristic
93C4⋊(C47⋊C8)D411yescharacteristic
94C4⋊(C47⋊C8)D411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093947C2×C411yescharacteristic
100#13093947C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102#13093945C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)D411yescharacteristic
113C22⋊(C47⋊C8)D411yescharacteristic
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116#13093935—21no—
117#13093935C2×C411yescharacteristic
118#13093935C2×C411yescharacteristic
119#13093934—21no—
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C2×#41×C47—21no—
126C2×M16×C47—21no—
127C22×C8×C47—21no—
128C4⋊Q8×C47C2×C411yescharacteristic
129#127×C47C2×C411yescharacteristic
130#124×C47—21no—
131#121×C47—21no—
132#121×C47C2×C411yescharacteristic
133#121×C47C2×C411yescharacteristic
134C4×D4×C47—21no—
135C4×D4×C47C2311yescharacteristic
136C4×D4×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—21no—
139C4⋊C8×C47C2311yescharacteristic
140C4⋊C8×C47C2311yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—81no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47C22×C411yescharacteristic
152C2×D4×C47C22×C411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C2×C22⋊D47—21no—
159C2×D188C22×C411yescharacteristic
160C2×C4×D47—21no—
161C2×Dic94C22×C411yescharacteristic
162M16×C47—81no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—42no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C22⋊C4×C47—21no—
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C42×C47C22×C411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47#4111yescharacteristic
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180#10625335—22no—
181#10625335—22no—
182#10625334—22no—
183#10625334—22no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194C4×Dic47—21no—
195#10625329—22no—
196#10625329—22no—
197#10625329—81no—
198#10625329—81no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—81no—
202C2×C47⋊C8—81no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210C2×C47⋊C8C2×D411yescharacteristic
211#10625324—81no—
212C8×D47—81no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47C4×D411yescharacteristic
216C22×D47—21no—
217Q8×C47—81no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—81no—
223D4×C47—81no—
224D4×C47—81no—
225D4×C47—81no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C23×C411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C22⋊D47—81no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247D188—21no—
248D188—21no—
249C4×D47—41no—
250C4×D47—41no—
251Dic94—21no—
252Dic94—21no—
253C8×C47—22no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265C47⋊C8#13112yes—
266C47⋊C8#13112yes—
267#17968—471nomaximal, Sylow
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47C2×C4×D411yescharacteristic
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47C2×#13111yescharacteristic
288C4×C47C2×#13111yescharacteristic
289C4×C47#57611yescharacteristic
290C4×C47#57711yescharacteristic
291Dic47—41no—
292Dic47—41no—
293Dic47—41no—
294#3171—471no—
295#2993—471no—
296#2981—471no—
297#1594—471no—
298#1592—471no—
299#1590—471no—
300#1589—471no—
301#1580—471no—
302SD16⋊C8—471no—
303C8×SD16—471no—
304C8×D8—471no—
305#1569—471no—
306#1494—471no—
307#1492D4711yescharacteristic, complemented
308C8×M16—471no—
309C2×C47—41no—
310C2×C47—81no—
311C2×C47—81no—
312C2×C47#293111yescharacteristic
313C2×C47#294611yescharacteristic
314C2×C47#295611yescharacteristic
315D47—81no—
316#532C2×D4711yescharacteristic
317#529—471no—
318#501—471no—
319#496—471no—
320#490—471no—
321#489—471no—
322#469—471no—
323#469—471no—
324#468—471no—
325#468—471no—
326#446—471no—
327C8×Q8—471no—
328C4×SD16—471no—
329C4×SD16—471no—
330C4×D8—471no—
331C4×D8—471no—
332#436—471no—
333#436—471no—
334#436—471no—
335#436—941no—
336#435—941no—
337#435—941no—
338#435—941no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—471no—
342#433—941no—
343#432—471no—
344#431—471no—
345#424—941no—
346#423C2×D4711yescharacteristic
347#408—941no—
348#408—941no—
349C4×M16—471no—
350C2×C4×C8C2×D4711yescharacteristic
351#335—471no—
352#335—471no—
353#334—471no—
354#334—471no—
355Q8⋊C8—471no—
356Q8⋊C8—471no—
357D4⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8C2×D4711yescharacteristic
360D4⋊C8C2×D4711yescharacteristic
361D4⋊C8C2×D4711yescharacteristic
362D4⋊C8C2×D4711yescharacteristic
363#322—471no—
364#322—471no—
365C82—471no—
366C82—471no—
367C47#1796811yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×SD16—471no—
370C2×SD16—471no—
371C2×D8—471no—
372C2×D8—471no—
373C2×M16—21no—
374C2×M16—471no—
375C2×M16—471no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C22×C8—21no—
380C22×C8—941no—
381C22×C8—941no—
382C22×C8—941no—
383C4⋊Q8C4×D4711yescharacteristic
384#127C4×D4711yescharacteristic
385#126—941no—
386#125—471no—
387#124—21no—
388#124—471no—
389#123—941no—
390C22⋊Q8—471no—
391#121—21no—
392#121—471no—
393#121C4×D4711yescharacteristic
394#121C4×D4711yescharacteristic
395C4×Q8—471no—
396C4×D4—21no—
397C4×D4—471no—
398C4×D4—941no—
399C4×D4C22×D4711yescharacteristic
400C4×D4C22×D4711yescharacteristic
401#117—941no—
402C2×C42C22×D4711yescharacteristic
403#107—471no—
404#107—471no—
405#106—471no—
406#106—471no—
407C4⋊C8—21no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—471no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8C22×D4711yescharacteristic
415C4⋊C8C22×D4711yescharacteristic
416#103—471no—
417#103—471no—
418#102—471no—
419#102—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424C22⋊C8—471no—
425C22⋊C8—471no—
426C22⋊C8—941no—
427C22⋊C8—941no—
428C22⋊C8—941no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433#97—471no—
434#97—471no—
435#97—941no—
436#97—941no—
437C4×C8—21no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—941no—
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—471no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—471no—
454C2×D4—941no—
455C2×D4C2×C4×D4711yescharacteristic
456C2×D4C2×C4×D4711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—941no—
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4D4×D4711yescharacteristic
462C22×C4#1062535211yescharacteristic
463SD16—942no—
464SD16—942no—
465D8—942no—
466D8—942no—
467M16—81no—
468M16—942no—
469M16—942no—
470M16—3761no—
471M16—3761no—
472M16—3761no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—471no—
482C2×C8—471no—
483C2×C8—471no—
484C2×C8—471no—
485C2×C8—471no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—3761no—
489C2×C8—3761no—
490C2×C8—3761no—
491C4⋊C4—21no—
492C4⋊C4—471no—
493C4⋊C4—471no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4C2×C4×D4711yescharacteristic
499C4⋊C4C2×C4×D4711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C42—941no—
510C42C2×C4×D4711yescharacteristic
511C42D4×D4711yescharacteristic
512C42#1062535211yescharacteristic
513C42C23×D4711yescharacteristic
514C23—21no—
515C23—21no—
516C23—941no—
517C23(C22⋊D47)⋊C411yescharacteristic
518Q8—81no—
519Q8—941no—
520Q8—941no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—941no—
530D4—941no—
531D4—3761no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4(C22⋊D47)⋊C411yescharacteristic
549C2×C4(C22⋊D47)⋊C411yescharacteristic
550C2×C4(C22⋊D47)⋊C411yescharacteristic
551C2×C4C22×C4×D4711yescharacteristic
552C2×C4C2×D4×D4711yescharacteristic
553C2×C4C2×#1062535211yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—472no—
559C8—472no—
560C8—941no—
561C8—941no—
562C8—941no—
563C8—941no—
564C8—941no—
565C8—941no—
566C8—1881no—
567C8—1881no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22C2×(C22⋊D47)⋊C411yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—1881no—
588C4—1881no—
589C4—1881no—
590C4#131×D4711yescharacteristic
591C4#131×D4711yescharacteristic
592C4#1568992411yescharacteristic
593C4#1568992911yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—3761no—
598C2#2025209611yescharacteristic
599C2#2025221411yescharacteristic
600C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1492C2
socleC22×C47C2×C4×D4
prime radical#20253977C2
cosocleC42×C47C24
hypercenter#1492D47
hypocenterC47#17968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #20252533C2semidirect
3. #20252464C2semidirect
4. #20242299C2semidirect
5. #20242287C2semidirect
6. #20242281C2semidirect
7. #20242270C2semidirect
8. #20242209C2semidirect
9. #20242197C2semidirect
10. #20242191C2semidirect
11. #20242180C2semidirect
12. #20242153C2semidirect
13. #20241849C2semidirect
14. C8×#10625329C2semidirect
15. C47×#1492C2semidirect
307. #1492D47semidirect
367. C47#17968semidirect

Maximal subgroups

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

subgroupindex
#202539772
#202525332
#202524642
#202422992
#202422872
#202422812
#202422702
#202422092
#202421972
#202421912
#202421802
#202421532
#202418492
C8×#106253292
C47×#14922
#1796847