Finite Group Databasebeta

← #26219401

Subgroups — #26219401

Order 12032.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689225C211yesmaximal, characteristic
2#20246032C211yesmaximal, characteristic
3#20245751C211yesmaximal, characteristic, complemented
4#20244016C211yesmaximal, characteristic
5#20244009C211yesmaximal, characteristic
6#20243981C211yesmaximal, characteristic, complemented
7#20243960C211yesmaximal, characteristic, complemented
8#20243742C211yesmaximal, characteristic
9#20243742C211yesmaximal, characteristic
10#20243659C211yesmaximal, characteristic, complemented
11#20243645C211yesmaximal, characteristic, complemented
12#20243285C211yesmaximal, characteristic, complemented
13C4×#13093949C211yesmaximal, characteristic, complemented
14C4×#13093946C211yesmaximal, characteristic
15C47×#1746C211yesmaximal, characteristic, complemented
16C22×#10625325C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19C2×C4×Dic94C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21#15689225C418yescomplemented
22C2×#13093958C2211yescharacteristic
23C2×#13093958C2211yescharacteristic
24C2×#13093956C2211yescharacteristic
25C2×#13093949C2211yescharacteristic
26C2×#13093949C2211yescharacteristic
27C2×#13093949C2211yescharacteristic
28C2×#13093946C2211yescharacteristic
29C2×#13093946C2211yescharacteristic
30C2×#13093946C2211yescharacteristic
31#15689025C2211yescharacteristic
32#15689025C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689012—21no—
36#15689012—21no—
37#15688985—21no—
38#15688982—21no—
39C4×C4⋊Dic47C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43#15688974—21no—
44#15688974—21no—
45#15688974—21no—
46#15688968—21no—
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53C2×#97×C47C2211yescharacteristic
54C2×C4×C8×C47C2211yescharacteristic
55C47×#376C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×Dic94C2311yescharacteristic
61C22×D188C2311yescharacteristic
62C22×C4×D47—21no—
63C2×#10625325—22no—
64C2×#10625325—22no—
65C2×#10625325C2×C414yes—
66C4×Dic94—22no—
67C4×Dic94—22no—
68C4×Dic94—22no—
69C4×Dic94—22no—
70C4×Dic94—22no—
71C4×Dic94C2×C414yes—
72C4×D188—22no—
73C4×D188C2×C414yes—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—21no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—21no—
97#13093958—22no—
98#13093958C2×C414yes—
99#13093956—22no—
100#13093949—22no—
101#13093949—22no—
102#13093949C2×C414yes—
103#13093946—22no—
104#13093946—22no—
105#13093946C2×C414yes—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119#97×C47C2×C414yes—
120C4×C8×C47—22no—
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124#95×C47D411yescharacteristic
125C23×D47—21no—
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2411yescharacteristic
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188C22×C412yes—
146C2×C4×D47—24no—
147C2×C4×D47—81no—
148C2×C4×D47—81no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94C22×C412yes—
153C2×Dic94#4112yes—
154C2×Dic94#4112yes—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47C22×C412yes—
166C2×C8×C47C22×C412yes—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47C22×C412yes—
172C42×C47#4112yes—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—81no—
175(C2×D47)⋊C4—81no—
176(C2×D47)⋊C4—81no—
177(C2×D47)⋊C4—81no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47C22×C412yes—
187C4⋊Dic47C22×C412yes—
188C4⋊Dic47#4112yes—
189C4⋊Dic47#4112yes—
190Dic47⋊C4—24no—
191Dic47⋊C4—24no—
192Dic47⋊C4—24no—
193Dic47⋊C4—81no—
194Dic47⋊C4—81no—
195C4×Dic47—24no—
196C4×Dic47—24no—
197C4×Dic47—24no—
198C4×Dic47—81no—
199C4×Dic47—81no—
200C4×Dic47—81no—
201C4×Dic47—81no—
202#10625325—28no—
203C23×C47C22×D411yescharacteristic
204C22×D47—22no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—41no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47C4×D412yes—
228C2×C4×C47C4×D412yes—
229C2×C4×C47C23×C411yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256D188—22no—
257D188—22no—
258D188—41no—
259D188—41no—
260C4×D47—84no—
261Dic94—22no—
262Dic94—22no—
263Dic94—22no—
264Dic94#11714yes—
265C8×C47—22no—
266C8×C47—22no—
267C8×C47—41no—
268C8×C47—41no—
269#21128—471nomaximal, Sylow
270C22×C47C2×C4×D411yescharacteristic
271C22×C47#52511yescharacteristic
272C22×C47#52511yescharacteristic
273C22×C47#57611yescharacteristic
274C22×C47#57711yescharacteristic
275C22×C47#57711yescharacteristic
276C22×C47#57811yescharacteristic
277C2×D47—42no—
278C2×D47—42no—
279C2×D47—42no—
280C2×D47—81no—
281C2×D47—81no—
282C2×D47—81no—
283C2×D47—81no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47C2×#11711yescharacteristic
291C4×C47C4×#4111yescharacteristic
292C4×C47#52911yescharacteristic
293C4×C47#52911yescharacteristic
294Dic47—24no—
295Dic47—42no—
296Dic47—42no—
297Dic47—42no—
298Dic47—42no—
299Dic47—81no—
300Dic47—81no—
301C2×#440—471no—
302#2319—471no—
303#2276—471no—
304#1926—471no—
305#1925—471no—
306#1921—471no—
307#1918—471no—
308#1880—471no—
309#1880—471no—
310#1865—471no—
311#1863—471no—
312#1776—471no—
313C4×#103—471no—
314C4×#102—471no—
315#1746D4711yescharacteristic, complemented
316C2×C47#229011yescharacteristic
317C2×C47#294611yescharacteristic
318C2×C47#294711yescharacteristic
319C2×C47#311911yescharacteristic
320C2×C47#312111yescharacteristic
321C2×C47#312411yescharacteristic
322C2×C47#312611yescharacteristic
323D47—82no—
324C22×SD16—471no—
325C2×C4×Q8—471no—
326C2×C4×Q8—471no—
327C2×C4×Q8—471no—
328C2×C4×D4—471no—
329#440—478no—
330C2×#107—471no—
331C2×#107—471no—
332C2×#106—471no—
333C2×#103—471no—
334C2×#103—471no—
335C2×#103—471no—
336C2×#102—471no—
337C2×#102—471no—
338C2×#102—471no—
339C2×#97C2×D4711yescharacteristic
340C2×C4×C8C2×D4711yescharacteristic
341#390—471no—
342#390—471no—
343#389—471no—
344#389—471no—
345#388—941no—
346#388—941no—
347#381—941no—
348#380—941no—
349C4×C4⋊C4—471no—
350C4×C4⋊C4—471no—
351C4×C4⋊C4—471no—
352C4×C4⋊C4—471no—
353C4×C4⋊C4—941no—
354C4×C4⋊C4—941no—
355C4×C4⋊C4—941no—
356#376—941no—
357#376C2×D4711yescharacteristic
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#336C2×D4711yescharacteristic
365#336C2×D4711yescharacteristic
366#336C2×D4711yescharacteristic
367#336C2×D4711yescharacteristic
368C47#2112811yescharacteristic, complemented, Sylow
369C22×Q8—471no—
370C22×D4—471no—
371C23×C4—941no—
372C2×SD16—474no—
373C2×SD16—942no—
374C2×SD16—942no—
375C22×C8C22×D4711yescharacteristic
376C22×C8C22×D4711yescharacteristic
377C22×C8C22×D4711yescharacteristic
378C22×C8C22×D4711yescharacteristic
379C4×Q8—474no—
380C4×Q8—942no—
381C4×Q8—942no—
382C4×Q8—942no—
383C4×Q8—942no—
384C4×Q8—942no—
385C4×D4—474no—
386C4×D4—942no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—941no—
400C2×C22⋊C4—941no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C42—941no—
404C2×C42—941no—
405C2×C42—941no—
406C2×C42—941no—
407C2×C42—941no—
408C2×C42—941no—
409C2×C42—941no—
410C2×C42C22×D4711yescharacteristic
411C2×C42C22×D4711yescharacteristic
412C2×C42C22×D4711yescharacteristic
413#107—474no—
414#107—942no—
415#106—942no—
416#103—474no—
417#103—942no—
418#103—942no—
419#102—474no—
420#102—942no—
421#102—942no—
422#97C4×D4714yes—
423C4×C8—22no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95—941no—
430#95D18811yescharacteristic
431#95D18811yescharacteristic
432#95D18811yescharacteristic
433#95D18811yescharacteristic
434C24—941no—
435C2×Q8—472no—
436C2×Q8—472no—
437C2×Q8—472no—
438C2×Q8—941no—
439C2×Q8—941no—
440C2×Q8—941no—
441C2×D4—472no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—941no—
446C2×D4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—944no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—3761no—
456C22×C4—3761no—
457C22×C4C2×D18811yescharacteristic
458C22×C4C2×D18811yescharacteristic
459C22×C4C2×D18811yescharacteristic
460C22×C4C2×D18811yescharacteristic
461C22×C4C2×D18811yescharacteristic
462C22×C4C2×D18811yescharacteristic
463C22×C4C23×D4711yescharacteristic
464SD16—948no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×C4×D4712yes—
476C2×C8C2×C4×D4712yes—
477C4⋊C4—472no—
478C4⋊C4—472no—
479C4⋊C4—472no—
480C4⋊C4—472no—
481C4⋊C4—944no—
482C4⋊C4—944no—
483C4⋊C4—944no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—3761no—
493C4⋊C4—3761no—
494C22⋊C4—944no—
495C22⋊C4—3761no—
496C22⋊C4—3761no—
497C22⋊C4—3761no—
498C22⋊C4—3761no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—944no—
504C42—944no—
505C42—944no—
506C42—3761no—
507C42—3761no—
508C42—3761no—
509C42—3761no—
510C42C2×C4×D4712yes—
511C42#1062535012yes—
512C23—942no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23—1881no—
518C23—1881no—
519C23C22×D18811yescharacteristic
520Q8—474no—
521Q8—942no—
522Q8—942no—
523Q8—942no—
524D4—942no—
525D4—942no—
526D4—1881no—
527D4—1881no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—3764no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4C4×D18812yes—
567C2×C4C4×D18812yes—
568C2×C4C22×C4×D4711yescharacteristic
569C2×C4#41×D4711yescharacteristic
570C2×C4#41×D4711yescharacteristic
571C2×C4#41×D4711yescharacteristic
572C2×C4#41×D4711yescharacteristic
573C2×C4C2×#1062535011yescharacteristic
574C8—22no—
575C8—22no—
576C8—41no—
577C8—41no—
578C22—3761no—
579C22—3761no—
580C22—3761no—
581C22—3761no—
582C22—1882no—
583C22—1882no—
584C22—1882no—
585C22C2×C4×D18811yescharacteristic
586C22#1568963511yescharacteristic
587C22#1568963511yescharacteristic
588C22#1568992811yescharacteristic
589C22#1568993511yescharacteristic
590C22#1568993511yescharacteristic
591C22#1568994011yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—944no—
599C4—3761no—
600C4—3761no—
601C4—1882no—
602C4—1882no—
603C4—1882no—
604C4—1882no—
605C4#117×D4711yescharacteristic
606C4#1568959111yescharacteristic
607C4#1568965111yescharacteristic
608C4#1568965111yescharacteristic
609C2—3762no—
610C2#2024583211yescharacteristic
611C2#2025222211yescharacteristic
612C2#2025223311yescharacteristic
613C2#2025358911yescharacteristic
614C2#2025361911yescharacteristic
615C2#2025365211yescharacteristic
616C2#2025368011yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1746C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#1746D47
hypocenterC47#21128
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
3. #20245751C2semidirect
6. #20243981C2semidirect
7. #20243960C2semidirect
10. #20243659C2semidirect
11. #20243645C2semidirect
12. #20243285C2semidirect
13. C4×#13093949C2semidirect
15. C47×#1746C2semidirect
21. #15689225C4semidirect
315. #1746D47semidirect
368. C47#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#156892252
#202460322
#202457512
#202440162
#202440092
#202439812
#202439602
#202437422
#202436592
#202436452
#202432852
C4×#130939492
C4×#130939462
C47×#17462
#2112847