Finite Group Databasebeta

← #26238125

Subgroups — #26238125

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689424C211yesmaximal, characteristic
2#20246482C211yesmaximal, characteristic, complemented
3#20246299C211yesmaximal, characteristic
4#20244353C211yesmaximal, characteristic, complemented
5#20244158C211yesmaximal, characteristic, complemented
6#20244121C211yesmaximal, characteristic, complemented
7#20244116C211yesmaximal, characteristic, complemented
8#20243981C211yesmaximal, characteristic, complemented
9#20243974C211yesmaximal, characteristic, complemented
10#20243652C211yesmaximal, characteristic
11#20243638C211yesmaximal, characteristic
12C4×#13093946C211yesmaximal, characteristic
13C4×#13093946C211yesmaximal, characteristic
14C4×#13093946C211yesmaximal, characteristic
15C8×C4⋊C4×C47C211yesmaximal, characteristic, complemented
16C2×#13094016C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20#15689424C418yescomplemented
21C2×#13093958C2211yescharacteristic
22C2×#13093958C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×#13093956C2211yescharacteristic
25C2×#13093946C2211yescharacteristic
26C2×#13093946C2211yescharacteristic
27C2×#13093946C2211yescharacteristic
28C2×#13093946C2211yescharacteristic
29#15689021C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689018—21no—
34#15689005—21no—
35#15689004—21no—
36#15688994—21no—
37#15688994—21no—
38#15688989C2211yescharacteristic
39#15688982—21no—
40C4×C4⋊Dic47C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43#15688974—21no—
44#95×D47—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53C2×C4⋊C8×C47C2211yescharacteristic
54C2×C4×C8×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47—21no—
63C22×C4×D47—21no—
64#13094016—22no—
65#13094016C2×C414yescomplemented
66C4×D188—22no—
67C4×D188—22no—
68C4×D188—22no—
69C4×D188—41no—
70C4×D188—41no—
71C4×D188C2×C414yes—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×Dic47⋊C4—21no—
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×C4×Dic47—21no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47—21no—
91#13093958—41no—
92#13093958C2×C414yescomplemented
93#13093956—41no—
94#13093956C2×C414yescomplemented
95#13093946—22no—
96#13093946C2×C414yes—
97#13093946C2×C414yes—
98#13093946Q814yes—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
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×C4⋊C4×C47D411yescharacteristic
113C2×C4⋊C4×C47D411yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C4⋊C8×C47C2×C414yescomplemented
118C4×C8×C47—22no—
119C4×C8×C47—41no—
120C4×C8×C47—41no—
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123C23×D47—21no—
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188C22×C412yes—
142C2×D188C2×Q812yes—
143C2×D188#4112yes—
144C2×C4×D47—24no—
145C2×C4×D47—42no—
146C2×C4×D47—42no—
147C2×C4×D47—42no—
148C2×C4×D47—42no—
149C2×C4×D47—81no—
150C2×C4×D47—81no—
151C2×C4×D47—81no—
152C2×C4×D47—81no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
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×C47C22×C412yes—
163C2×C8×C47C22×C412yes—
164C2×C8×C47C2×Q812yes—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
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—42no—
175(C2×D47)⋊C4—42no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
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⋊Dic47C22×C412yes—
189C4⋊Dic47C2×Q812yes—
190Dic47⋊C4—24no—
191Dic47⋊C4—24no—
192Dic47⋊C4—42no—
193Dic47⋊C4—81no—
194Dic47⋊C4—81no—
195Dic47⋊C4—81no—
196C4×Dic47—42no—
197C4×Dic47—81no—
198C4×Dic47—81no—
199C23×C47C22×D411yescharacteristic
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—22no—
203C22×D47—41no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
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×C47C4×D412yes—
222C2×C4×C47C4×D412yes—
223C2×C4×C47#13512yes—
224C2×C4×C47#13512yes—
225C2×C4×C47C23×C411yescharacteristic
226C2×C4×C47C22×Q811yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C2×C4×C47H(5,𝔽2)11yescharacteristic
230C2×C4×C472−1+411yescharacteristic
231C2×Dic47—22no—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—41no—
236C2×Dic47—41no—
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—
252D188—22no—
253D188—22no—
254D188—22no—
255D188C4×Q814yes—
256C4×D47—84no—
257C4×D47—84no—
258C4×D47—84no—
259C8×C47—22no—
260C8×C47—22no—
261C8×C47—22no—
262C8×C47—41no—
263#22966—471nomaximal, Sylow
264C22×C47C2×C4×D411yescharacteristic
265C22×C47#54611yescharacteristic
266C22×C47D4×Q811yescharacteristic
267C22×C47C2×#13511yescharacteristic
268C22×C47C2×#13511yescharacteristic
269C22×C47#57611yescharacteristic
270C22×C47#57711yescharacteristic
271C2×D47—24no—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—42no—
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47C2×C4×Q811yescharacteristic
285C4×C47#52011yescharacteristic
286C4×C47#55211yescharacteristic
287C4×C47#55411yescharacteristic
288Dic47—42no—
289Dic47—42no—
290Dic47—42no—
291Dic47—42no—
292Dic47—81no—
293Dic47—81no—
294Dic47—81no—
295C2×#478—471no—
296#2370—471no—
297#2349—471no—
298#1991—471no—
299#1949—471no—
300#1942—471no—
301#1941—471no—
302#1921—471no—
303#1920—471no—
304#1864—471no—
305#1862—471no—
306C8×C4⋊C4D4711yescharacteristic, complemented
307C4×#102—471no—
308C4×#102—471no—
309C4×#102—471no—
310C2×C47#236011yescharacteristic
311C2×C47C4×#13511yescharacteristic
312C2×C47#294611yescharacteristic
313C2×C47#329611yescharacteristic
314C2×C47#329711yescharacteristic
315C2×C47#338011yescharacteristic
316C2×C47#338111yescharacteristic
317D47—44no—
318C2×#125—471no—
319C2×C4×D4—471no—
320C2×C4×D4—471no—
321C2×C4×D4—471no—
322#478—478no—
323C2×#107—471no—
324C2×#107—471no—
325C2×#106—471no—
326C2×#106—471no—
327C2×C4⋊C8C2×D4711yescharacteristic
328C2×#102—471no—
329C2×#102—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×C4×C8C2×D4711yescharacteristic
333C2×C4×C8C2×D4711yescharacteristic
334C2×C4×C8C2×D4711yescharacteristic
335#389—471no—
336#389—471no—
337#389—471no—
338#389—471no—
339#389—941no—
340#387—941no—
341#387—941no—
342#385—941no—
343#385—941no—
344#382—471no—
345#380—941no—
346C4×C4⋊C4—471no—
347C4×C4⋊C4—471no—
348C4×C4⋊C4—471no—
349C4×C4⋊C4—941no—
350C4×C4⋊C4C2×D4711yescharacteristic
351C2×#95—941no—
352#340—471no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340—471no—
358#340—471no—
359#340—471no—
360#336C2×D4711yescharacteristic
361#336C2×D4711yescharacteristic
362C47#2296611yescharacteristic, complemented, Sylow
363C22×D4—471no—
364C23×C4—941no—
365C23×C4—941no—
366C23×C4—941no—
367C22×C8C22×D4711yescharacteristic
368C22×C8C22×D4711yescharacteristic
369C22×C8C22×D4711yescharacteristic
370C22×C8C22×D4711yescharacteristic
371#125—474no—
372#125—942no—
373C4×D4—474no—
374C4×D4—942no—
375C4×D4—942no—
376C4×D4—942no—
377C4×D4—1881no—
378C4×D4—1881no—
379C2×C4⋊C4—471no—
380C2×C4⋊C4—471no—
381C2×C4⋊C4—471no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4D18811yescharacteristic
393C2×C4⋊C4D18811yescharacteristic
394C2×C22⋊C4—941no—
395C2×C22⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C42—941no—
398C2×C42—941no—
399C2×C42—941no—
400C2×C42C22×D4711yescharacteristic
401C2×C42C22×D4711yescharacteristic
402C2×C42C22×D4711yescharacteristic
403#107—474no—
404#107—1881no—
405#106—474no—
406#106—1881no—
407C4⋊C8C4×D4714yescomplemented
408#102—474no—
409#102—474no—
410#102—474no—
411#102—942no—
412C4×C8—22no—
413C4×C8—41no—
414C4×C8—41no—
415#95—941no—
416#95—941no—
417#95—941no—
418#95—941no—
419#95—941no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95—941no—
424#95D18811yescharacteristic
425#95D18811yescharacteristic
426C24—941no—
427C2×D4—472no—
428C2×D4—472no—
429C2×D4—472no—
430C2×D4—941no—
431C2×D4—941no—
432C2×D4—941no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—944no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—3761no—
442C22×C4—3761no—
443C22×C4—3761no—
444C22×C4—3761no—
445C22×C4—1882no—
446C22×C4—1882no—
447C22×C4—1882no—
448C22×C4—1882no—
449C22×C4C2×D18811yescharacteristic
450C22×C4C2×D18811yescharacteristic
451C22×C4C2×D18811yescharacteristic
452C22×C4C2×D18811yescharacteristic
453C22×C4C2×D18811yescharacteristic
454C22×C4C2×D18811yescharacteristic
455C22×C4C23×D4711yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8C2×C4×D4712yes—
466C2×C8C2×C4×D4712yes—
467C2×C8Q8×D4712yes—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—472no—
471C4⋊C4—472no—
472C4⋊C4—472no—
473C4⋊C4—472no—
474C4⋊C4—944no—
475C4⋊C4—944no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—3761no—
487C4⋊C4—3761no—
488C4⋊C4—3761no—
489C4⋊C4—1882no—
490C22⋊C4—944no—
491C22⋊C4—1882no—
492C22⋊C4—1882no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—3761no—
498C42—3761no—
499C42—1882no—
500C42C2×C4×D4712yes—
501C42#1062535012yes—
502C23—942no—
503C23—942no—
504C23—942no—
505C23—1881no—
506C23—1881no—
507C23—1881no—
508C23—1881no—
509C23C22×D18811yescharacteristic
510D4—474no—
511D4—942no—
512D4—942no—
513D4—942no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—942no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—3764no—
533C2×C4—3764no—
534C2×C4—3764no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4—1881no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
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×C4C4×D18812yes—
553C2×C4C4×D18812yes—
554C2×C4#1309404612yes—
555C2×C4#1309404612yes—
556C2×C4C22×C4×D4711yescharacteristic
557C2×C4C2×Q8×D4711yescharacteristic
558C2×C4#41×D4711yescharacteristic
559C2×C4C2×#1062535011yescharacteristic
560C2×C4#1309406911yescharacteristic
561C2×C4#1309407111yescharacteristic
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C22—944no—
567C22—1882no—
568C22—1882no—
569C22—1882no—
570C22—1882no—
571C22—1882no—
572C22—1882no—
573C22C2×C4×D18811yescharacteristic
574C22#1568976811yescharacteristic
575C22Q8×D18811yescharacteristic
576C22C2×#1309404611yescharacteristic
577C22C2×#1309404611yescharacteristic
578C22#1568992811yescharacteristic
579C22#1568993511yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—3761no—
587C4—3761no—
588C4—3761no—
589C4—1882no—
590C4—1882no—
591C4—1882no—
592C4—1882no—
593C4C4×Q8×D4711yescharacteristic
594C4#1568960211yescharacteristic
595C4#1568981211yescharacteristic
596C4#1568982811yescharacteristic
597C2—1884no—
598C2#2024639511yescharacteristic
599C2C4×#1309404611yescharacteristic
600C2#2025222211yescharacteristic
601C2#2025522511yescharacteristic
602C2#2025524011yescharacteristic
603C2#2025625611yescharacteristic
604C2#2025626511yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC8×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenterC8×C4⋊C4D47
hypocenterC47#22966
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20246482C2semidirect
4. #20244353C2semidirect
5. #20244158C2semidirect
6. #20244121C2semidirect
7. #20244116C2semidirect
8. #20243981C2semidirect
9. #20243974C2semidirect
15. C8×C4⋊C4×C47C2semidirect
20. #15689424C4semidirect
65. #13094016C2×C4semidirect
92. #13093958C2×C4semidirect
94. #13093956C2×C4semidirect
117. C4⋊C8×C47C2×C4semidirect
306. C8×C4⋊C4D47semidirect
362. C47#22966semidirect
407. C4⋊C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894242
#202464822
#202462992
#202443532
#202441582
#202441212
#202441162
#202439812
#202439742
#202436522
#202436382
C4×#130939462
C8×C4⋊C4×C472
#2296647