Finite Group Databasebeta

← #26187157

Subgroups — #26187157

Order 12032.

576 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253954C211yesmaximal, characteristic
2#20252540C211yesmaximal, characteristic, complemented
3#20252538C211yesmaximal, characteristic, complemented
4#20242257C211yesmaximal, characteristic, complemented
5#20242256C211yesmaximal, characteristic, complemented
6#20242255C211yesmaximal, characteristic, complemented
7#20242252C211yesmaximal, characteristic, complemented
8#20242233C211yesmaximal, characteristic, complemented
9#20242232C211yesmaximal, characteristic, complemented
10#20242223C211yesmaximal, characteristic, complemented
11#20242142C211yesmaximal, characteristic, complemented
12#20241852C211yesmaximal, characteristic, complemented
13#20241850C211yesmaximal, characteristic, complemented
14#20241679C211yesmaximal, characteristic, complemented
15C47×#1582C211yesmaximal, characteristic, complemented
16#15689660C2211yescharacteristic
17#15689655C2211yescharacteristic
18#15689523C411yescharacteristic
19#15689504C411yescharacteristic
20#15689479C411yescharacteristic
21#15689476C411yescharacteristic
22#15689363C411yescharacteristic
23#15689358C411yescharacteristic
24#15689353C411yescharacteristic
25#15689349C411yescharacteristic
26#15689250C2211yescharacteristic
27Q8×C47⋊C8C2211yescharacteristic
28C8×Dic94C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625325C2211yescharacteristic
31C4×#10625334C2211yescharacteristic
32#15689202C2211yescharacteristic
33#15689201C2211yescharacteristic
34#15689200—21no—
35#15689198—21no—
36#15689196—21no—
37#15689194—21no—
38#15689188C2211yescharacteristic
39#15689185—21no—
40#15689181—21no—
41#15689174C2211yescharacteristic
42#15689174C2211yescharacteristic
43#15689149—21no—
44#15689148—21no—
45#15689145C2211yescharacteristic
46#15689145C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688874C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688845C2211yescharacteristic
59#15688844C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625325C2×C411yescharacteristic
69C2×#10625334C2×C411yescharacteristic
70C2×#10625329—21no—
71C2×#10625324—21no—
72C2×#10625324—21no—
73C2×#10625324—21no—
74C2×C8×D47—21no—
75C2×C8×D47C2×C411yescharacteristic
76C2×C8×D47C2×C411yescharacteristic
77#13094019—21no—
78#13094017—21no—
79#13094015C2×C411yescharacteristic
80#13094015C2×C411yescharacteristic
81#13094013C2×C411yescharacteristic
82#13094011C2×C411yescharacteristic
83#13094009—21no—
84#13094006—21no—
85#13094004C2×C411yescharacteristic
86#13094000C2×C411yescharacteristic
87#13093999C2×C411yescharacteristic
88#13093995C2×C411yescharacteristic
89C4×Dic94C2311yescharacteristic
90C4×D188—21no—
91C4×D188C2311yescharacteristic
92C4×C22⋊D47—21no—
93#13093983—21no—
94#13093981—21no—
95C42×D47C2311yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093956C2×C411yescharacteristic
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8D411yescharacteristic
108Dic47⋊C8D411yescharacteristic
109#13093949C2×C411yescharacteristic
110#13093948C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093945C2×C411yescharacteristic
114#13093944C2×C411yescharacteristic
115C22⋊(C47⋊C8)—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8D411yescharacteristic
120(C2×D47)⋊C8D411yescharacteristic
121#13093934—21no—
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C8×Dic47—21no—
127C8×Dic47C2×C411yescharacteristic
128C8×Dic47C2×C411yescharacteristic
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
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47C22×C411yescharacteristic
146C22×C4×C47—21no—
147C2×C22⋊D47—21no—
148C2×D188—21no—
149C2×D188C22×C411yescharacteristic
150C2×C4×D47—21no—
151C2×C4×D47C22×C411yescharacteristic
152C2×C4×D47C2×D411yescharacteristic
153C2×C4×D47#4111yescharacteristic
154C2×Dic94C22×C411yescharacteristic
155SD16×C47—41no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—81no—
160C2×C8×C47C22×C411yescharacteristic
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C2×D411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C4⋊C4×C47—21no—
165C4⋊C4×C47C22×C411yescharacteristic
166C4⋊C4×C47C22×C411yescharacteristic
167C22⋊C4×C47—21no—
168C42×C47—21no—
169C42×C47C2411yescharacteristic
170C22⋊Dic47—21no—
171C22⋊Dic47—21no—
172C22⋊Dic47—21no—
173#10625337—41no—
174#10625334—41no—
175(C2×D47)⋊C4—21no—
176(C2×D47)⋊C4—21no—
177(C2×D47)⋊C4—21no—
178(C2×D47)⋊C4—21no—
179(C2×D47)⋊C4—21no—
180(C2×D47)⋊C4—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47C22×C411yescharacteristic
185C4⋊Dic47C22×C411yescharacteristic
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47C22×C411yescharacteristic
192C4×Dic47C2×D411yescharacteristic
193C4×Dic47#4111yescharacteristic
194#10625329—81no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202#10625325—41no—
203#10625324—81no—
204#10625324—81no—
205#10625324—81no—
206C8×D47—41no—
207C8×D47—41no—
208C8×D47—81no—
209C23×C47—21no—
210C22×D47—21no—
211C22×D47C4×D411yescharacteristic
212Q8×C47—21no—
213Q8×C47—21no—
214D4×C47—21no—
215D4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47C23×C411yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C47C2×#4111yescharacteristic
224C22⋊D47—81no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47C4×D411yescharacteristic
229C2×Dic47C4×D411yescharacteristic
230C2×Dic47C4×D411yescharacteristic
231D188—21no—
232D188—21no—
233D188—81no—
234C4×D47—21no—
235C4×D47—21no—
236C4×D47—21no—
237C4×D47—21no—
238C4×D47—41no—
239C4×D47—41no—
240C4×D47—41no—
241Dic94—21no—
242Dic94—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—41no—
255C47⋊C8—41no—
256C47⋊C8—41no—
257#17993—471nomaximal, Sylow
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47C2×C4×D411yescharacteristic
262C2×D47—21no—
263C2×D47—21no—
264C2×D47—21no—
265C2×D47—41no—
266C2×D47—41no—
267C2×D47—41no—
268C4×C47—21no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47#56811yescharacteristic
273C4×C47#56811yescharacteristic
274C4×C47#57711yescharacteristic
275C4×C47#57711yescharacteristic
276Dic47—21no—
277Dic47—21no—
278Dic47—21no—
279Dic47—41no—
280Dic47—41no—
281Dic47—41no—
282#3168—471no—
283#2993—471no—
284#2993—471no—
285#1587—471no—
286#1587—471no—
287#1586—471no—
288#1586—471no—
289#1583—471no—
290#1583—471no—
291#1582—471no—
292#1582D4711yescharacteristic, complemented
293#1566—471no—
294#1495—471no—
295#1495—471no—
296#1452—471no—
297C2×C47—81no—
298C2×C47#293211yescharacteristic
299C2×C47#295211yescharacteristic
300C2×C47#295711yescharacteristic
301D47—41no—
302D47—81no—
303#529—471no—
304#529—471no—
305#499—471no—
306#495—471no—
307#488—471no—
308#488—471no—
309#467—471no—
310#466—471no—
311#465—471no—
312#465—471no—
313#446—471no—
314#446C2×D4711yescharacteristic
315C8×Q8—471no—
316C8×Q8—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16C2×D4711yescharacteristic
320C4×D8—471no—
321#436—471no—
322#436—471no—
323#436—941no—
324#436—941no—
325#435—941no—
326#435—941no—
327C8×D4—471no—
328C8×D4C2×D4711yescharacteristic
329#433—941no—
330#433—941no—
331#431—471no—
332#431—471no—
333#424—941no—
334#424—941no—
335#423—471no—
336#423—471no—
337C2×C4×C8—471no—
338#334—471no—
339#334—471no—
340#334—471no—
341#334C2×D4711yescharacteristic
342Q8⋊C8—471no—
343Q8⋊C8—471no—
344Q8⋊C8—471no—
345Q8⋊C8C2×D4711yescharacteristic
346D4⋊C8—471no—
347D4⋊C8—471no—
348D4⋊C8—471no—
349D4⋊C8C2×D4711yescharacteristic
350#322—471no—
351#322—471no—
352#322—471no—
353#322C2×D4711yescharacteristic
354C47#1799311yescharacteristic, complemented, Sylow
355C2×Q16—471no—
356C2×SD16—471no—
357C2×SD16C4×D4711yescharacteristic
358C2×D8—471no—
359C2×M16—941no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C22×C8—21no—
364C22×C8—471no—
365C22×C8—471no—
366C22×C8—941no—
367#126—941no—
368#126—941no—
369#125—471no—
370#125—471no—
371#124—471no—
372#124—471no—
373#123—941no—
374#123—941no—
375C22⋊Q8—471no—
376C22⋊Q8—471no—
377#121—471no—
378#121—471no—
379C4×Q8—471no—
380C4×Q8C22×D4711yescharacteristic
381C4×D4—471no—
382C4×D4—941no—
383C4×D4—941no—
384C4×D4C22×D4711yescharacteristic
385#117—941no—
386#117—941no—
387C2×C42—471no—
388#107—471no—
389#107—471no—
390#106—471no—
391#106C4×D4711yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—471no—
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—941no—
398C4⋊C8—941no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8C22×D4711yescharacteristic
404C4⋊C8C22×D4711yescharacteristic
405#103—471no—
406#103—471no—
407#103—471no—
408#103C4×D4711yescharacteristic
409#102—471no—
410#102—471no—
411#102—471no—
412#102C4×D4711yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—471no—
415C22⋊C8—471no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—21no—
421#97—941no—
422C4×C8—471no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—941no—
428C4×C8—941no—
429C4×C8C22×D4711yescharacteristic
430C4×C8C22×D4711yescharacteristic
431C4×C8C22×D4711yescharacteristic
432C2×Q8—471no—
433C2×Q8C2×C4×D4711yescharacteristic
434C2×D4—471no—
435C2×D4—941no—
436C2×D4—941no—
437C2×D4C2×C4×D4711yescharacteristic
438C22×C4—21no—
439C22×C4—471no—
440C22×C4—471no—
441C22×C4—471no—
442C22×C4—941no—
443Q16—1881no—
444SD16—41no—
445SD16—1881no—
446D8—1881no—
447M16—3761no—
448M16—3761no—
449M16—3761no—
450M16—3761no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—471no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—3761no—
463C2×C8—1881no—
464C2×C8—1881no—
465C2×C8C2×C4×D4711yescharacteristic
466C2×C8C2×C4×D4711yescharacteristic
467C2×C8D4×D4711yescharacteristic
468C2×C8D4×D4711yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—471no—
471C4⋊C4—471no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4C2×C4×D4711yescharacteristic
480C4⋊C4C2×C4×D4711yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—941no—
483C22⋊C4—941no—
484C22⋊C4—941no—
485C22⋊C4—941no—
486C22⋊C4—941no—
487C22⋊C4—941no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C42—21no—
492C42—471no—
493C42—471no—
494C42—471no—
495C42—941no—
496C42C23×D4711yescharacteristic
497C23—21no—
498C23—471no—
499C23—941no—
500Q8—21no—
501Q8—21no—
502Q8—941no—
503Q8—941no—
504D4—21no—
505D4—21no—
506D4—941no—
507D4—941no—
508D4—3761no—
509D4—3761no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—471no—
516C2×C4—471no—
517C2×C4—471no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—941no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4C22×C4×D4711yescharacteristic
529C2×C4C2×D4×D4711yescharacteristic
530C2×C4#41×D4711yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—941no—
539C8—941no—
540C8—941no—
541C8—941no—
542C8—1881no—
543C8—1881no—
544C8—1881no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—941no—
549C22—941no—
550C22—941no—
551C22—1881no—
552C22—1881no—
553C22—1881no—
554C22C4×D4×D4711yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—941no—
560C4—941no—
561C4—941no—
562C4—1881no—
563C4—1881no—
564C4—1881no—
565C4#1568988811yescharacteristic
566C4#1568988911yescharacteristic
567C4#1568992911yescharacteristic
568C4#1568993011yescharacteristic
569C2—81no—
570C2—3761no—
571C2—1881no—
572C2#2025210211yescharacteristic
573C2#2025226611yescharacteristic
574C2#2025230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1582C2
socleC22×C47C2×C4×D4
prime radical#15689358C4
cosocleC42×C47C24
hypercenter#1582D47
hypocenterC47#17993
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. #20252540C2semidirect
3. #20252538C2semidirect
4. #20242257C2semidirect
5. #20242256C2semidirect
6. #20242255C2semidirect
7. #20242252C2semidirect
8. #20242233C2semidirect
9. #20242232C2semidirect
10. #20242223C2semidirect
11. #20242142C2semidirect
12. #20241852C2semidirect
13. #20241850C2semidirect
14. #20241679C2semidirect
15. C47×#1582C2semidirect
292. #1582D47semidirect
354. C47#17993semidirect

Maximal subgroups

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

subgroupindex
#202539542
#202525402
#202525382
#202422572
#202422562
#202422552
#202422522
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C47×#15822
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