Finite Group Databasebeta

← #26252384

Subgroups — #26252384

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic
2C2×#15689418C211yesmaximal, characteristic, complemented
3C4×#13094000C211yesmaximal, characteristic
4#20244728C212yesmaximal, complemented
5#20244537C212yesmaximal, complemented
6#20244341C211yesmaximal, characteristic, complemented
7#20244335C211yesmaximal, characteristic, complemented
8#20243697C212yesmaximal
9#20243586C212yesmaximal
10#20243365C211yesmaximal, characteristic
11C2×C47×#475C211yesmaximal, characteristic, complemented
12#15689678—24no—
13#15689678—24no—
14C2×#13094024C2211yescharacteristic
15C2×#13094015C2212yes—
16C2×#13094004—21no—
17C2×#13094000—21no—
18C2×#13094000C2211yescharacteristic
19C2×Q8×Dic47—21no—
20C2×#13093989—21no—
21C2×#13093982C2212yes—
22C2×C42×D47C2211yescharacteristic
23#15689418—24no—
24C2×#13093957C2212yes—
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093948C2212yes—
27C2×(C2×D47)⋊C8C2212yes—
28#15689030C2211yescharacteristic
29#15689019C2211yescharacteristic
30#15689004—21no—
31#15688994—21no—
32#15688980C2211yescharacteristic
33C4×Dic47⋊C4—21no—
34C4×C4⋊Dic47C2211yescharacteristic
35C4×(C2×D47)⋊C4—21no—
36#15688886C2212yes—
37#15688886C2212yes—
38#15688885C2212yes—
39#15688885C2212yes—
40#15688877C2212yes—
41C2×C4⋊Q8×C47C2211yescharacteristic
42C2×C4×Q8×C47C2211yescharacteristic
43C47×#475—24no—
44C2×#106×C47C2212yes—
45C2×C4⋊C8×C47C2211yescharacteristic
46C2×#103×C47C2212yes—
47C22×Dic94—21no—
48C22×C4×D47D411yescharacteristic
49C22×C4×D47D411yescharacteristic
50C22×C4×D47C2311yescharacteristic
51C22×C47⋊C8C2312yes—
52#13094024—22no—
53#13094024D414yes—
54#13094015—24no—
55#13094015—24no—
56#13094004—28no—
57#13094000—28no—
58#13094000—22no—
59#13094000Q814yescomplemented
60Q8×Dic47—28no—
61#13093989—28no—
62#13093982—24no—
63#13093982—24no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2312yes—
68C2×C4⋊Dic47C2311yescharacteristic
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—22no—
71C2×Dic47⋊C4—21no—
72C2×(C2×D47)⋊C4—21no—
73C2×(C2×D47)⋊C4—22no—
74C2×(C2×D47)⋊C4—21no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47D411yescharacteristic
78C2×C4×Dic47D411yescharacteristic
79C2×C4×Dic47C2311yescharacteristic
80C42×D47—22no—
81C42×D47—22no—
82#13093957—24no—
83C4⋊(C47⋊C8)—22no—
84#13093948—24no—
85(C2×D47)⋊C8—24no—
86C47⋊#95—21no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C22×Q8×C47—21no—
92C22×Q8×C47C2311yescharacteristic
93C22×C8×C47C2312yes—
94C4⋊Q8×C47—22no—
95C4⋊Q8×C47D414yes—
96C4×Q8×C47—22no—
97C4×Q8×C47—22no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2312yes—
102C2×C42×C47—21no—
103C2×C42×C47C2311yescharacteristic
104#106×C47—24no—
105C4⋊C8×C47—22no—
106#103×C47—24no—
107C23×D47C2×D411yescharacteristic
108C2×Q8×C47—24no—
109C2×Q8×C47—21no—
110C2×Q8×C47—21no—
111C2×Q8×C47—21no—
112C2×Q8×C47—21no—
113C2×Q8×C47—21no—
114C2×Q8×C47—42no—
115C2×Q8×C47—42no—
116C2×Q8×C47C2×Q812yes—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2411yescharacteristic
123C22×Dic47—21no—
124C22×Dic47—22no—
125C22×Dic47—21no—
126C22×Dic47C2×D411yescharacteristic
127C22×Dic47C2×D411yescharacteristic
128C22×Dic47C2×D411yescharacteristic
129C2×C4×D47—21no—
130C2×C4×D47—21no—
131C2×C4×D47—21no—
132C2×C4×D47—21no—
133C2×C4×D47—22no—
134C2×C4×D47—22no—
135C2×C4×D47—22no—
136C2×C4×D47—22no—
137C2×C4×D47—41no—
138C2×C4×D47—41no—
139C2×C4×D47C2×Q812yes—
140C2×C4×D47#4112yes—
141C2×Dic94—24no—
142C2×Dic94—42no—
143C2×Dic94—42no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C4⋊C4×C47—24no—
148C4⋊C4×C47—22no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—42no—
152C4⋊C4×C47C2×D414yes—
153C42×C47—42no—
154C42×C47C2×D412yes—
155C42×C47C2×D412yes—
156(C2×D47)⋊C4—28no—
157(C2×D47)⋊C4—24no—
158(C2×D47)⋊C4—42no—
159C4⋊Dic47—28no—
160C4⋊Dic47—24no—
161C4⋊Dic47—22no—
162C4⋊Dic47—21no—
163C4⋊Dic47—21no—
164C4⋊Dic47—21no—
165C4⋊Dic47C2×D414yes—
166C4⋊Dic47C2×Q812yes—
167Dic47⋊C4—28no—
168Dic47⋊C4—24no—
169Dic47⋊C4—42no—
170C4×Dic47—28no—
171C4×Dic47—22no—
172C4×Dic47—22no—
173C4×Dic47—21no—
174C4×Dic47—21no—
175C4×Dic47—42no—
176C2×C47⋊C8—22no—
177C2×C47⋊C8—22no—
178C2×C47⋊C8—22no—
179C23×C47C22×D411yescharacteristic
180C22×D47—21no—
181C22×D47—21no—
182C22×D47—21no—
183C22×D47—21no—
184C22×D47—21no—
185C22×D47—21no—
186C22×D47C22⋊Q812yes—
187Q8×C47—22no—
188Q8×C47—22no—
189Q8×C47—41no—
190Q8×C47—41no—
191Q8×C47—48no—
192C2×C4×C47—21no—
193C2×C4×C47—21no—
194C2×C4×C47—24no—
195C2×C4×C47—22no—
196C2×C4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47#12012yes—
204C2×C4×C47#12012yes—
205C2×C4×C47#13512yes—
206C2×C4×C47#13712yes—
207C2×C4×C47C22×D411yescharacteristic
208C2×C4×C47C22×D411yescharacteristic
209C2×C4×C47C22×Q811yescharacteristic
210C2×C4×C47C2×#4111yescharacteristic
211C2×C4×C472−1+411yescharacteristic
212C2×C4×C472−1+411yescharacteristic
213C2×Dic47—21no—
214C2×Dic47—21no—
215C2×Dic47—21no—
216C2×Dic47—21no—
217C2×Dic47—24no—
218C2×Dic47—22no—
219C2×Dic47—21no—
220C2×Dic47—21no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—41no—
224C2×Dic47—41no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—41no—
228C2×Dic47—41no—
229C2×Dic47—41no—
230C2×Dic47C22⋊Q812yes—
231C4×D47—22no—
232C4×D47—22no—
233C4×D47—22no—
234C4×D47—22no—
235C4×D47—44no—
236C4×D47—44no—
237Dic94—48no—
238C8×C47—42no—
239C47⋊C8—42no—
240#24303—471nomaximal, Sylow
241C22×C47C2×#12011yescharacteristic
242C22×C47C2×C22⋊Q811yescharacteristic
243C22×C47#53611yescharacteristic
244C22×C47C2×#13511yescharacteristic
245C22×C47C2×#13711yescharacteristic
246C22×C47#57511yescharacteristic
247C22×C47#57511yescharacteristic
248C2×D47—22no—
249C2×D47—22no—
250C2×D47—22no—
251C2×D47—41no—
252C2×D47—41no—
253C2×D47—41no—
254C2×D47—41no—
255C4×C47—22no—
256C4×C47—42no—
257C4×C47—44no—
258C4×C47—81no—
259C4×C47#45214yes—
260C4×C47#54811yescharacteristic
261C4×C47#54811yescharacteristic
262C4×C47D4×Q811yescharacteristic
263C4×C47D4×Q811yescharacteristic
264Dic47—22no—
265Dic47—42no—
266Dic47—41no—
267Dic47—44no—
268Dic47—41no—
269Dic47—81no—
270C2×#533—471no—
271C2×#477—471no—
272C2×#475D4711yescharacteristic, complemented
273C4×C22⋊Q8—471no—
274#2059—472no—
275#2026—472no—
276#1988—471no—
277#1987—471no—
278#1873—472no—
279#1854—472no—
280#1797—471no—
281C2×C47#240911yescharacteristic
282C2×C47C2×#45211yescharacteristic
283C2×C47#300511yescharacteristic
284C2×C47#307611yescharacteristic
285C2×C47#307811yescharacteristic
286C2×C47#323311yescharacteristic
287C2×C47#323711yescharacteristic
288D47—42no—
289#533—944no—
290#533—944no—
291C2×C4⋊Q8—471no—
292C2×C4⋊Q8C2×D4711yescharacteristic
293C2×#125—472no—
294C2×C22⋊Q8—471no—
295C2×C22⋊Q8—941no—
296C2×C22⋊Q8—941no—
297C2×C4×Q8—941no—
298C2×C4×Q8—941no—
299C2×C4×Q8C2×D4711yescharacteristic
300C2×#117—472no—
301C22×C42—471no—
302#477—944no—
303#475—24no—
304C2×#107—472no—
305C2×#106C2×D4712yes—
306C2×C4⋊C8—471no—
307C2×C4⋊C8C2×D4711yescharacteristic
308C2×#103—472no—
309C2×#103C2×D4712yes—
310C2×C22⋊C8—472no—
311#391—471no—
312#389—471no—
313#387—941no—
314#385—941no—
315#380—471no—
316C4×C4⋊C4—471no—
317C4×C4⋊C4—941no—
318C4×C22⋊C4—941no—
319#340—472no—
320#340—472no—
321#340—472no—
322#340—472no—
323#336—472no—
324C47#2430311yescharacteristic, complemented, Sylow
325C22×Q8—21no—
326C22×Q8—941no—
327C22×Q8C22×D4711yescharacteristic
328C23×C4—471no—
329C23×C4—471no—
330C23×C4—471no—
331C22×C8—472no—
332C22×C8C22×D4712yes—
333C4⋊Q8—22no—
334C4⋊Q8—474no—
335C4⋊Q8—942no—
336C4⋊Q8C22⋊D4714yes—
337#125—944no—
338#125—944no—
339C22⋊Q8—474no—
340C22⋊Q8—948no—
341C22⋊Q8—942no—
342C22⋊Q8—948no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—948no—
346C4×Q8—948no—
347#117—944no—
348#117—944no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—472no—
352C2×C4⋊C4—471no—
353C2×C4⋊C4—471no—
354C2×C4⋊C4—942no—
355C2×C4⋊C4—942no—
356C2×C4⋊C4—941no—
357C2×C4⋊C4—941no—
358C2×C4⋊C4—941no—
359C2×C4⋊C4C22×D4711yescharacteristic
360C2×C4⋊C4C22×D4712yes—
361C2×C22⋊C4—942no—
362C2×C22⋊C4—941no—
363C2×C22⋊C4—941no—
364C2×C42—21no—
365C2×C42—471no—
366C2×C42—471no—
367C2×C42—471no—
368C2×C42—942no—
369C2×C42—942no—
370C2×C42—942no—
371C2×C42—941no—
372C2×C42C22×D4711yescharacteristic
373#107—944no—
374#106—24no—
375C4⋊C8—22no—
376C4⋊C8—942no—
377#103—24no—
378#103—944no—
379C22⋊C8—944no—
380#95—941no—
381#95—941no—
382#95—941no—
383#95—941no—
384#95—941no—
385C24—471no—
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—944no—
395C2×Q8—1882no—
396C2×Q8—1882no—
397C2×Q8Q8×D4712yes—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—471no—
402C22×C4—472no—
403C22×C4—472no—
404C22×C4—471no—
405C22×C4—471no—
406C22×C4—941no—
407C22×C4—941no—
408C22×C4—941no—
409C22×C4—941no—
410C22×C4—941no—
411C22×C4—942no—
412C22×C4—942no—
413C22×C4—942no—
414C22×C4—942no—
415C22×C4—942no—
416C22×C4—941no—
417C22×C4—1881no—
418C22×C4—1881no—
419C22×C4D4×D4711yescharacteristic
420C22×C4D4×D4711yescharacteristic
421C22×C4C23×D4711yescharacteristic
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—942no—
426C2×C8—942no—
427C2×C8—942no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—42no—
433C4⋊C4—474no—
434C4⋊C4—472no—
435C4⋊C4—944no—
436C4⋊C4—948no—
437C4⋊C4—948no—
438C4⋊C4—944no—
439C4⋊C4—942no—
440C4⋊C4—941no—
441C4⋊C4—941no—
442C4⋊C4—941no—
443C4⋊C4—1882no—
444C4⋊C4C2×C22⋊D4714yes—
445C22⋊C4—944no—
446C22⋊C4—948no—
447C22⋊C4—1882no—
448C42—42no—
449C42—948no—
450C42—942no—
451C42—942no—
452C42—941no—
453C42—941no—
454C42—1882no—
455C42D4×D4712yes—
456C42C2×C22⋊D4712yes—
457C23—472no—
458C23—941no—
459C23—941no—
460C23—941no—
461C23—941no—
462C23—941no—
463C23—941no—
464C23C2×D4×D4711yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—41no—
468Q8—41no—
469Q8—48no—
470Q8—1888no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—472no—
483C2×C4—941no—
484C2×C4—941no—
485C2×C4—942no—
486C2×C4—942no—
487C2×C4—942no—
488C2×C4—942no—
489C2×C4—941no—
490C2×C4—941no—
491C2×C4—944no—
492C2×C4—942no—
493C2×C4—941no—
494C2×C4—941no—
495C2×C4—941no—
496C2×C4—941no—
497C2×C4—1884no—
498C2×C4—1881no—
499C2×C4—1881no—
500C2×C4—1881no—
501C2×C4—1881no—
502C2×C4—1881no—
503C2×C4—1882no—
504C2×C4—1882no—
505C2×C4—1884no—
506C2×C4#1309399212yes—
507C2×C4#1309399212yes—
508C2×C4#1309404512yes—
509C2×C4#1309405312yes—
510C2×C4C2×D4×D4711yescharacteristic
511C2×C4C22×C22⋊D4711yescharacteristic
512C2×C4C2×Q8×D4711yescharacteristic
513C2×C4#41×D4711yescharacteristic
514C2×C4#1309407111yescharacteristic
515C2×C4#1309407211yescharacteristic
516C8—42no—
517C8—1882no—
518C22—942no—
519C22—942no—
520C22—942no—
521C22—1881no—
522C22—1881no—
523C22—1881no—
524C22—1881no—
525C22C2×#1309399211yescharacteristic
526C22C22⋊Q8×D4711yescharacteristic
527C22#1568969611yescharacteristic
528C22C2×#1309404511yescharacteristic
529C22C2×#1309405311yescharacteristic
530C22#1568992211yescharacteristic
531C22#1568992211yescharacteristic
532C4—22no—
533C4—44no—
534C4—42no—
535C4—81no—
536C4—942no—
537C4—3761no—
538C4—1881no—
539C4—1881no—
540C4—1884no—
541C4—1882no—
542C4#1568928214yes—
543C4#1568978011yescharacteristic
544C4#1568978311yescharacteristic
545C4#1568978611yescharacteristic
546C4Q8×C22⋊D4711yescharacteristic
547C2—1882no—
548C2#2024674911yescharacteristic
549C2C2×#1568928211yescharacteristic
550C2#2025262911yescharacteristic
551C2#2025317111yescharacteristic
552C2#2025318811yescharacteristic
553C2#2025457111yescharacteristic
554C2#2025460111yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#475C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#475D47
hypocenterC47#24303
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#15689418C2semidirect
4. #20244728C2semidirect
5. #20244537C2semidirect
6. #20244341C2semidirect
7. #20244335C2semidirect
11. C2×C47×#475C2semidirect
59. #13094000Q8semidirect
272. C2×#475D47semidirect
324. C47#24303semidirect

Maximal subgroups

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

subgroupindex
C2×#156896782
C2×#156894182
C4×#130940002
#202447282
#202445372
#202443412
#202443352
#202436972
#202435862
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C2×C47×#4752
#2430347