Finite Group Databasebeta

← #26224276

Subgroups — #26224276

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689478C211yesmaximal, characteristic
2#20246129C211yesmaximal, characteristic, complemented
3#20246099C211yesmaximal, characteristic
4#20244357C211yesmaximal, characteristic, complemented
5#20244204C211yesmaximal, characteristic
6#20244085C211yesmaximal, characteristic
7#20244078C211yesmaximal, characteristic, complemented
8#20244071C211yesmaximal, characteristic
9#20244064C211yesmaximal, characteristic, complemented
10#20243516C211yesmaximal, characteristic, complemented
11#20243219C211yesmaximal, characteristic, complemented
12#20243214C211yesmaximal, characteristic
13C4×#13093949C211yesmaximal, characteristic, complemented
14C4×#13093946C211yesmaximal, characteristic
15C47×#1726C211yesmaximal, characteristic, complemented
16C2×#13094016C2211yescharacteristic
17C2×#13094012C2211yescharacteristic
18C2×C4×Dic94C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20#15689478C418yescomplemented
21C2×#13093949C2211yescharacteristic
22C2×#13093949C2211yescharacteristic
23C2×#13093949C2211yescharacteristic
24C2×#13093949C2211yescharacteristic
25C2×#13093946C2211yescharacteristic
26C2×#13093946C2211yescharacteristic
27C2×#13093946C2211yescharacteristic
28C2×#13093946C2211yescharacteristic
29#15689029C2211yescharacteristic
30#15689025C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689020—21no—
34#15689020—21no—
35#15689015—21no—
36#15689015—21no—
37#15689010—21no—
38#15689010—21no—
39#15688997—21no—
40#15688997—21no—
41#15688993C2211yescharacteristic
42#15688993C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53C2×#97×C47C2211yescharacteristic
54C2×#97×C47C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C2×C4×C8×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic
59C47×#376C2211yescharacteristic
60C22×Dic94C2311yescharacteristic
61C22×D188C2311yescharacteristic
62C22×C4×D47—21no—
63#13094016—22no—
64#13094016C2×C414yescomplemented
65#13094012—22no—
66#13094012C2×C414yes—
67C4×Dic94—22no—
68C4×Dic94—22no—
69C4×D188—22no—
70C4×D188—22no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93C2×C4×Dic47—21no—
94#13093949—22no—
95#13093949—22no—
96#13093949C2×C414yescomplemented
97#13093949C2×C414yescomplemented
98#13093946—22no—
99#13093946—22no—
100#13093946C2×C414yes—
101#13093946C2×C414yes—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C22×C8×C47C2311yescharacteristic
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115#97×C47—22no—
116#97×C47—22no—
117#97×C47—22no—
118C4×C8×C47—22no—
119C4×C8×C47—22no—
120C4×C8×C47C2×C414yescomplemented
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—42no—
147C2×C4×D47—81no—
148C2×C4×D47—81no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94C22×C412yes—
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×C47C22×C412yes—
164C2×C8×C47C22×C412yes—
165C2×C8×C47#4112yes—
166C2×C8×C47#4112yes—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47C22×C412yes—
170C42×C47#4112yes—
171C42×C47#4112yes—
172C42×C47#4112yes—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—24no—
175(C2×D47)⋊C4—42no—
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⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—81no—
189C4⋊Dic47—81no—
190C4⋊Dic47—81no—
191C4⋊Dic47—81no—
192C4⋊Dic47C22×C412yes—
193C4⋊Dic47C22×C412yes—
194Dic47⋊C4—24no—
195Dic47⋊C4—24no—
196Dic47⋊C4—42no—
197Dic47⋊C4—81no—
198Dic47⋊C4—81no—
199C4×Dic47—42no—
200C4×Dic47—81no—
201C4×Dic47—81no—
202C23×C47C22×D411yescharacteristic
203C22×D47—22no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C2×C4×C47—21no—
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×C47C4×D412yes—
225C2×C4×C47C4×D412yes—
226C2×C4×C47#12412yes—
227C2×C4×C47#12412yes—
228C2×C4×C47C23×C411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
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—
255D188—22no—
256D188—22no—
257D188—41no—
258D188—41no—
259C4×D47—84no—
260Dic94—22no—
261Dic94—22no—
262Dic94—41no—
263Dic94—41no—
264C8×C47—22no—
265C8×C47—22no—
266C8×C47—22no—
267C8×C47—22no—
268#21643—471nomaximal, Sylow
269C22×C47C2×C4×D411yescharacteristic
270C22×C47C2×#12411yescharacteristic
271C22×C47#53211yescharacteristic
272C22×C47#57611yescharacteristic
273C22×C47#57711yescharacteristic
274C22×C47#57711yescharacteristic
275C22×C47#57811yescharacteristic
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—42no—
279C2×D47—81no—
280C2×D47—81no—
281C2×D47—81no—
282C2×D47—81no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47C4×#4111yescharacteristic
290C4×C47C4×#4111yescharacteristic
291C4×C47#52911yescharacteristic
292C4×C47#52911yescharacteristic
293Dic47—42no—
294Dic47—42no—
295Dic47—42no—
296Dic47—81no—
297Dic47—81no—
298Dic47—81no—
299Dic47—81no—
300C2×#488—471no—
301#2330—471no—
302#2326—471no—
303#1992—471no—
304#1959—471no—
305#1936—471no—
306#1935—471no—
307#1934—471no—
308#1933—471no—
309#1834—471no—
310#1763—471no—
311#1762—471no—
312C4×#103—471no—
313C4×#102—471no—
314#1726D4711yescharacteristic, complemented
315C2×C47C4×#12411yescharacteristic
316C2×C47#295111yescharacteristic
317C2×C47#295211yescharacteristic
318C2×C47#313611yescharacteristic
319C2×C47#313711yescharacteristic
320C2×C47#317811yescharacteristic
321C2×C47#317911yescharacteristic
322D47—82no—
323C2×#125—471no—
324C2×#124—471no—
325C2×C4×Q8—471no—
326C2×C4×D4—471no—
327#488—478no—
328C2×#103—471no—
329C2×#103—471no—
330C2×#103—471no—
331C2×#103—471no—
332C2×#102—471no—
333C2×#102—471no—
334C2×#102—471no—
335C2×#102—471no—
336C2×#97C2×D4711yescharacteristic
337C2×#97C2×D4711yescharacteristic
338C2×#97C2×D4711yescharacteristic
339C2×C4×C8C2×D4711yescharacteristic
340C2×C4×C8C2×D4711yescharacteristic
341C2×C4×C8C2×D4711yescharacteristic
342#391—471no—
343#390—471no—
344#389—471no—
345#389—471no—
346#389—941no—
347#389—941no—
348#388—941no—
349#388—941no—
350#387—941no—
351#387—941no—
352#385—941no—
353#385—941no—
354#384—471no—
355#384—471no—
356C4×C4⋊C4—471no—
357C4×C4⋊C4—471no—
358#376C2×D4711yescharacteristic
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367C47#2164311yescharacteristic, complemented, Sylow
368C22×Q8—471no—
369C22×D4—471no—
370C23×C4—941no—
371C22×C8C22×D4711yescharacteristic
372C22×C8C22×D4711yescharacteristic
373C22×C8C22×D4711yescharacteristic
374C22×C8C22×D4711yescharacteristic
375#125—474no—
376#125—942no—
377#124—474no—
378#124—942no—
379C4×Q8—942no—
380C4×Q8—942no—
381C4×D4—942no—
382C4×D4—942no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
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×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408C2×C42C22×D4711yescharacteristic
409#103—474no—
410#103—474no—
411#103—942no—
412#103—942no—
413#102—474no—
414#102—474no—
415#102—942no—
416#102—942no—
417#97—22no—
418#97—22no—
419#97—22no—
420C4×C8—22no—
421C4×C8—22no—
422C4×C8C4×D4714yescomplemented
423#95—941no—
424#95—941no—
425#95—941no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95D18811yescharacteristic
430#95D18811yescharacteristic
431#95D18811yescharacteristic
432#95D18811yescharacteristic
433C24—941no—
434C2×Q8—472no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×Q8—941no—
440C2×D4—472no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—3761no—
454C22×C4—3761no—
455C22×C4—1882no—
456C22×C4C2×D18811yescharacteristic
457C22×C4C2×D18811yescharacteristic
458C22×C4C2×D18811yescharacteristic
459C22×C4C2×D18811yescharacteristic
460C22×C4C2×D18811yescharacteristic
461C22×C4C2×D18811yescharacteristic
462C22×C4C23×D4711yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×C4×D4712yes—
472C2×C8C2×C4×D4712yes—
473C2×C8#1062535012yes—
474C2×C8#1062535012yes—
475C4⋊C4—472no—
476C4⋊C4—472no—
477C4⋊C4—944no—
478C4⋊C4—944no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—3761no—
490C4⋊C4—3761no—
491C4⋊C4—3761no—
492C4⋊C4—3761no—
493C4⋊C4—3761no—
494C4⋊C4—3761no—
495C4⋊C4—1882no—
496C22⋊C4—944no—
497C22⋊C4—944no—
498C22⋊C4—3761no—
499C22⋊C4—3761no—
500C22⋊C4—1882no—
501C42—21no—
502C42—21no—
503C42—3761no—
504C42—3761no—
505C42—1882no—
506C42C2×C4×D4712yes—
507C42#1062535012yes—
508C42#1062535012yes—
509C42#1062535012yes—
510C23—942no—
511C23—1881no—
512C23—1881no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23C22×D18811yescharacteristic
518Q8—942no—
519Q8—942no—
520Q8—1881no—
521Q8—1881no—
522D4—942no—
523D4—942no—
524D4—1881no—
525D4—1881no—
526C2×C4—21no—
527C2×C4—21no—
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—942no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—3764no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
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×C4C4×D18812yes—
563C2×C4C4×D18812yes—
564C2×C4#1309401212yes—
565C2×C4#1309401212yes—
566C2×C4C22×C4×D4711yescharacteristic
567C2×C4C2×#1062535011yescharacteristic
568C2×C4C2×#1062535011yescharacteristic
569C2×C4C2×#1062535011yescharacteristic
570C2×C4C2×#1062535011yescharacteristic
571C2×C4C2×#1062535011yescharacteristic
572C8—22no—
573C8—22no—
574C8—22no—
575C8—22no—
576C22—3761no—
577C22—3761no—
578C22—3761no—
579C22—3761no—
580C22—1882no—
581C22—1882no—
582C22—1882no—
583C22C2×C4×D18811yescharacteristic
584C22C2×#1309401211yescharacteristic
585C22#1568967311yescharacteristic
586C22#1568992811yescharacteristic
587C22#1568993511yescharacteristic
588C22#1568993511yescharacteristic
589C22#1568994011yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—3761no—
597C4—3761no—
598C4—3761no—
599C4—3761no—
600C4—1882no—
601C4—1882no—
602C4—1882no—
603C4C4×#1062535011yescharacteristic
604C4C4×#1062535011yescharacteristic
605C4#1568965711yescharacteristic
606C4#1568965711yescharacteristic
607C2—3762no—
608C2C4×#1309401211yescharacteristic
609C2#2025226511yescharacteristic
610C2#2025227311yescharacteristic
611C2#2025374411yescharacteristic
612C2#2025375511yescharacteristic
613C2#2025405611yescharacteristic
614C2#2025407111yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1726C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#1726D47
hypocenterC47#21643
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #20246129C2semidirect
4. #20244357C2semidirect
7. #20244078C2semidirect
9. #20244064C2semidirect
10. #20243516C2semidirect
11. #20243219C2semidirect
13. C4×#13093949C2semidirect
15. C47×#1726C2semidirect
20. #15689478C4semidirect
64. #13094016C2×C4semidirect
96. #13093949C2×C4semidirect
97. #13093949C2×C4semidirect
120. C4×C8×C47C2×C4semidirect
314. #1726D47semidirect
367. C47#21643semidirect
422. C4×C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894782
#202461292
#202460992
#202443572
#202442042
#202440852
#202440782
#202440712
#202440642
#202435162
#202432192
#202432142
C4×#130939492
C4×#130939462
C47×#17262
#2164347