Finite Group Databasebeta

← #26238152

Subgroups — #26238152

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689401C211yesmaximal, characteristic
2#20246447C211yesmaximal, characteristic, complemented
3D4×Dic47⋊C4C211yesmaximal, characteristic
4#20244347C211yesmaximal, characteristic, complemented
5#20244150C211yesmaximal, characteristic, complemented
6#20244126C211yesmaximal, characteristic, complemented
7#20244125C211yesmaximal, characteristic, complemented
8#20243980C211yesmaximal, characteristic, complemented
9#20243979C211yesmaximal, characteristic, complemented
10#20243651C211yesmaximal, characteristic
11#20243649C211yesmaximal, characteristic
12#20243256C211yesmaximal, characteristic, complemented
13#20243215C211yesmaximal, characteristic
14#102×Dic47C211yesmaximal, characteristic
15C47×#1762C211yesmaximal, characteristic
16C2×#13094023C2211yescharacteristic
17C2×C4×Dic94—21no—
18C2×D4×Dic47C2211yescharacteristic
19C2×D4×Dic47C2211yescharacteristic
20C22×Dic47⋊C4—21no—
21#15689401C418yescomplemented
22C2×#13093958C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093956C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093934C2211yescharacteristic
30C2×C8×Dic47C2211yescharacteristic
31#15689027—21no—
32#15689022C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689019C2211yescharacteristic
36#15689010—21no—
37#15689007—21no—
38#15688996—21no—
39#15688995—21no—
40#15688992C2211yescharacteristic
41#15688981—21no—
42C4⋊C4×Dic47C2211yescharacteristic
43C4⋊C4×Dic47C2211yescharacteristic
44C4×Dic47⋊C4C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#102×C47C2211yescharacteristic
56C2×#97×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C22×Dic94—21no—
61C23×Dic47—21no—
62C23×Dic47—21no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13094023—22no—
66#13094023C2×C414yescomplemented
67C4×Dic94—44no—
68D4×Dic47—22no—
69D4×Dic47—22no—
70D4×Dic47—41no—
71D4×Dic47C2×C414yes—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—44no—
84C2×Dic47⋊C4D411yescharacteristic
85C2×Dic47⋊C4D411yescharacteristic
86C2×C22⋊Dic47—21no—
87C2×C22⋊Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47C2311yescharacteristic
91C2×C4×Dic47C2311yescharacteristic
92#13093958C2×C414yescomplemented
93#13093957C2×C414yescomplemented
94#13093956—41no—
95#13093955—41no—
96Dic47⋊C8C2×C414yescomplemented
97#13093945—22no—
98#13093945C2×C414yes—
99#13093934—41no—
100C8×Dic47—22no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95D411yescharacteristic
108C47⋊#95D411yescharacteristic
109C22×D4×C47C2311yescharacteristic
110C23×C4×C47—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C4×D4×C47—22no—
114C4×D4×C47—41no—
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—21no—
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121#102×C47C2×C414yes—
122#102×C47Q814yescomplemented
123#97×C47—41no—
124#95×C47—21no—
125C24×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47C22×C412yes—
130C2×D4×C47C2×Q812yes—
131C2×D4×C47#4112yes—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47—81no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2411yescharacteristic
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—24no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—42no—
147C22×Dic47—42no—
148C22×Dic47—42no—
149C22×Dic47—42no—
150C22×Dic47—81no—
151C22×Dic47C2×D411yescharacteristic
152C22×Dic47C2×D411yescharacteristic
153C22×Dic47C2×D411yescharacteristic
154C22×Dic47C2×D411yescharacteristic
155C2×Dic94—24no—
156C2×Dic94—42no—
157C2×Dic94—42no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47C22×C412yes—
163C2×C8×C47C2×Q812yes—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47C22×C412yes—
169C4⋊C4×C47C2×Q812yes—
170C22⋊C4×C47—42no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—42no—
174C22⋊Dic47—24no—
175C22⋊Dic47—42no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—42no—
183C4⋊Dic47C22×C412yes—
184C4⋊Dic47C22×C412yes—
185Dic47⋊C4—24no—
186Dic47⋊C4—22no—
187Dic47⋊C4—22no—
188Dic47⋊C4—42no—
189Dic47⋊C4—42no—
190Dic47⋊C4—42no—
191Dic47⋊C4—42no—
192Dic47⋊C4—81no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—42no—
196C4×Dic47—42no—
197C4×Dic47C22×C412yes—
198C4×Dic47#4112yes—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8C22×C412yes—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47C22×D411yescharacteristic
213D4×C47—22no—
214D4×C47—22no—
215D4×C47—22no—
216D4×C47C4×Q814yescomplemented
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—22no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—84no—
233C2×C4×C47C23×C411yescharacteristic
234C2×C4×C47C22×Q811yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47H(5,𝔽2)11yescharacteristic
238C2×C4×C472−1+411yescharacteristic
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—48no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—84no—
261C2×Dic47C4×D412yes—
262C2×Dic47C4×D412yes—
263C2×Dic47AGL(1,ℤ/8)12yes—
264C2×Dic47AGL(1,ℤ/8)12yes—
265Dic94—48no—
266C8×C47—22no—
267C8×C47—22no—
268C47⋊C8—22no—
269C47⋊C8—41no—
270#22968—471nomaximal, Sylow
271C22×C47—24no—
272C22×C47—42no—
273C22×C47—42no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47—42no—
277C22×C47—42no—
278C22×C47C2×C4×D411yescharacteristic
279C22×C47#54611yescharacteristic
280C22×C47D4×Q811yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C47#57711yescharacteristic
284C22×C47#57811yescharacteristic
285C4×C47—41no—
286C4×C47—42no—
287C4×C47—42no—
288C4×C47—41no—
289C4×C47—81no—
290C4×C47C2×C4×Q811yescharacteristic
291C4×C47#52011yescharacteristic
292C4×C47#55211yescharacteristic
293C4×C47#55411yescharacteristic
294Dic47—22no—
295Dic47—41no—
296Dic47—42no—
297Dic47—42no—
298Dic47—41no—
299Dic47—81no—
300Dic47—81no—
301Dic47#44214yes—
302C2×#474—471no—
303#2365—471no—
304D4×C4⋊C4—471no—
305#1990—471no—
306#1948—471no—
307#1943—471no—
308#1943—471no—
309#1921—471no—
310#1921—471no—
311#1864—471no—
312#1864—471no—
313#1770—471no—
314#1762—471no—
315#1762D4711yescharacteristic
316C4×#102—471no—
317C2×C47—44no—
318C2×C47#236011yescharacteristic
319C2×C47C2×#44211yescharacteristic
320C2×C47#294711yescharacteristic
321C2×C47#332411yescharacteristic
322C2×C47#333011yescharacteristic
323C2×C47#338411yescharacteristic
324C2×C47#338611yescharacteristic
325C2×C4⋊Q8—471no—
326C2×C4×Q8—941no—
327C2×C4×D4—471no—
328C2×C4×D4—471no—
329C2×C4×D4C2×D4711yescharacteristic
330C22×C4⋊C4—941no—
331#474—478no—
332C2×#107—471no—
333C2×#107—471no—
334C2×#106—471no—
335C2×#106—471no—
336C2×C4⋊C8—471no—
337C2×#102—471no—
338C2×#102—471no—
339C2×#102C2×D4711yescharacteristic
340C2×#102C2×D4711yescharacteristic
341C2×#97—471no—
342C2×#97C2×D4711yescharacteristic
343C2×C4×C8—471no—
344#391—941no—
345#389—471no—
346#389—471no—
347#389—471no—
348#389—471no—
349#387—941no—
350#387—941no—
351#385—941no—
352#385—941no—
353#384—471no—
354#380—941no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4—471no—
357C4×C4⋊C4—471no—
358C4×C4⋊C4C2×D4711yescharacteristic
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340C2×D4711yescharacteristic
366#340C2×D4711yescharacteristic
367#336—471no—
368#336—471no—
369C47#2296811yescharacteristic, complemented, Sylow
370C22×Q8—941no—
371C22×D4C22×D4711yescharacteristic
372C23×C4—21no—
373C23×C4—941no—
374C23×C4—941no—
375C22×C8—471no—
376C22×C8—471no—
377C22×C8C22×D4711yescharacteristic
378C22×C8C22×D4711yescharacteristic
379C4⋊Q8—474no—
380C4⋊Q8—942no—
381C4×Q8—1884no—
382C4×D4—22no—
383C4×D4—41no—
384C4×D4—474no—
385C4×D4—942no—
386C4×D4—942no—
387C4×D4—1881no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—1884no—
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C4⋊C4C22×D4711yescharacteristic
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—941no—
407C2×C22⋊C4—941no—
408C2×C42—21no—
409C2×C42—471no—
410C2×C42—471no—
411C2×C42—941no—
412C2×C42—941no—
413C2×C42C22×D4711yescharacteristic
414#107—474no—
415#107—474no—
416#106—1881no—
417#106—1881no—
418C4⋊C8—474no—
419#102—474no—
420#102—942no—
421#102Dic9414yescomplemented
422#102C4×D4714yes—
423#97—41no—
424#97—1881no—
425C4×C8—942no—
426#95—21no—
427#95—471no—
428#95—471no—
429#95—941no—
430#95—941no—
431#95—941no—
432#95—941no—
433#95—941no—
434#95—941no—
435C24—21no—
436C2×Q8—944no—
437C2×Q8—1882no—
438C2×Q8—1882no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×Dic9412yes—
443C2×D4C2×C4×D4712yes—
444C2×D4#1062535012yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—81no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—944no—
456C22×C4—941no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—3761no—
461C22×C4—1882no—
462C22×C4—1882no—
463C22×C4—1882no—
464C22×C4—1882no—
465C22×C4D4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4C23×D4711yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—472no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8C2×Dic9412yes—
479C2×C8C2×C4×D4712yes—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—472no—
485C4⋊C4—472no—
486C4⋊C4—942no—
487C4⋊C4—942no—
488C4⋊C4—944no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—3761no—
496C4⋊C4—1882no—
497C4⋊C4—1882no—
498C4⋊C4—1882no—
499C4⋊C4—1882no—
500C4⋊C4—1882no—
501C4⋊C4C2×Dic9412yes—
502C4⋊C4C2×C4×D4712yes—
503C22⋊C4—42no—
504C22⋊C4—944no—
505C22⋊C4—1882no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—472no—
510C42—472no—
511C42—941no—
512C42—941no—
513C42—1882no—
514C42—1882no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23C2×D4×D4711yescharacteristic
523Q8—1888no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4C4×Dic9414yescomplemented
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—84no—
544C2×C4—472no—
545C2×C4—472no—
546C2×C4—472no—
547C2×C4—472no—
548C2×C4—941no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—941no—
555C2×C4—941no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—3764no—
559C2×C4—1888no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4C22×C4×D4711yescharacteristic
571C2×C4C22×Dic9411yescharacteristic
572C2×C4#41×D4711yescharacteristic
573C2×C4C2×#1062535011yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309407111yescharacteristic
576C8—22no—
577C8—22no—
578C8—942no—
579C8—1881no—
580C22—24no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22C4×D4×D4711yescharacteristic
588C22#1568976311yescharacteristic
589C22D4×Dic9411yescharacteristic
590C22AGL(1,ℤ/8)×D4711yescharacteristic
591C22AGL(1,ℤ/8)×D4711yescharacteristic
592C22#1568993311yescharacteristic
593C22#1568993911yescharacteristic
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—474no—
600C4—942no—
601C4—3761no—
602C4—3761no—
603C4—1882no—
604C4—1882no—
605C4—1881no—
606C4—1881no—
607C4C2×C4×Dic9411yescharacteristic
608C4#1568960211yescharacteristic
609C4#1568980611yescharacteristic
610C4#1568983211yescharacteristic
611C2—44no—
612C2#2024639411yescharacteristic
613C2#442×D4711yescharacteristic
614C2#2025222811yescharacteristic
615C2#2025561511yescharacteristic
616C2#2025568911yescharacteristic
617C2#2025628811yescharacteristic
618C2#2025631011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1762C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
cosocleC22×C4×C47C24
hypercenter#1762D47
hypocenterC47#22968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #20246447C2semidirect
4. #20244347C2semidirect
5. #20244150C2semidirect
6. #20244126C2semidirect
7. #20244125C2semidirect
8. #20243980C2semidirect
9. #20243979C2semidirect
12. #20243256C2semidirect
21. #15689401C4semidirect
66. #13094023C2×C4semidirect
92. #13093958C2×C4semidirect
93. #13093957C2×C4semidirect
96. Dic47⋊C8C2×C4semidirect
122. #102×C47Q8semidirect
216. D4×C47C4×Q8semidirect
369. C47#22968semidirect
421. #102Dic94semidirect
527. D4C4×Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×#156894012
#202464472
D4×Dic47⋊C42
#202443472
#202441502
#202441262
#202441252
#202439802
#202439792
#202436512
#202436492
#202432562
#202432152
#102×Dic472
C47×#17622
#2296847