Finite Group Databasebeta

← #26110806

Subgroups — #26110806

Order 12032.

768 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
2C4×#13093995C211yesmaximal, characteristic
3C4×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
4C2×D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5#20241228C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C2×C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×C8×D47—21no—
9C2×#13093995C411yescharacteristic
10C2×C4×C22⋊D47—21no—
11C2×C42×D47C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×Dic47⋊C8—21no—
14C4⋊C8×D47—22no—
15C4⋊C8×D47—22no—
16C2×(C2×D47)⋊C8—21no—
17C2×C4×C47⋊C8C2211yescharacteristic
18#15689026C411yescharacteristic
19#15689019C411yescharacteristic
20#15689011—21no—
21#15688999—21no—
22#15688980C411yescharacteristic
23C4×C4⋊Dic47C2211yescharacteristic
24C4×C22⋊Dic47—21no—
25#15688877—21no—
26D4⋊(C47⋊C8)—22no—
27C2×C4×D4×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C47×D4⋊C8—22no—
31C22×C22⋊D47—21no—
32C22×C4×D47C2×C411yescharacteristic
33C22×C4×D47D411yescharacteristic
34C22×C4×D47D411yescharacteristic
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C2×C8×D47—24no—
38C2×C8×D47—42no—
39C2×C8×D47—42no—
40#13093995—22no—
41#13093995C814yescomplemented
42C4×C22⋊D47—42no—
43C4×C22⋊D47—42no—
44C2×C4⋊Dic47C2×C411yescharacteristic
45C2×C4⋊Dic47C2×C411yescharacteristic
46C2×Dic47⋊C4—21no—
47C2×C22⋊Dic47—21no—
48C2×C22⋊Dic47—21no—
49C2×C22⋊Dic47—21no—
50C2×(C2×D47)⋊C4—21no—
51C2×C4×Dic47—21no—
52C2×C4×Dic47C2×C411yescharacteristic
53C2×C4×Dic47D411yescharacteristic
54C2×C4×Dic47D411yescharacteristic
55C42×D47—21no—
56C42×D47—21no—
57C42×D47—21no—
58C42×D47—21no—
59C4⋊(C47⋊C8)—21no—
60C4⋊(C47⋊C8)D412yescomplemented
61Dic47⋊C8—24no—
62(C2×D47)⋊C8—24no—
63C4×C47⋊C8—21no—
64C4×C47⋊C8—21no—
65C47⋊#95—21no—
66C47⋊#95—21no—
67C47⋊#95—21no—
68C22×D4×C47C2×C411yescharacteristic
69C23×C4×C47—21no—
70C22×C8×C47—21no—
71C22×C8×C47—21no—
72C4×D4×C47—21no—
73C4×D4×C47—21no—
74C4×D4×C47—21no—
75C4×D4×C47—21no—
76C2×C4⋊C4×C47C2×C411yescharacteristic
77C2×C22⋊C4×C47—21no—
78C2×C42×C47C2311yescharacteristic
79C4⋊C8×C47—21no—
80C4⋊C8×C47D412yescomplemented
81C4×C8×C47—21no—
82C4×C8×C47—21no—
83C24×C47—21no—
84C23×D47C22⋊C411yescharacteristic
85C2×D4×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—21no—
88C2×D4×C47—21no—
89C2×D4×C47—21no—
90C2×D4×C47C2×C812yescomplemented
91C22×C4×C47—21no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47C22×C411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C2×C22⋊D47—24no—
102C2×C22⋊D47—42no—
103C2×C22⋊D47—42no—
104C22×Dic47—21no—
105C22×Dic47—21no—
106C22×Dic47C22⋊C411yescharacteristic
107C22×Dic47C22⋊C411yescharacteristic
108C22×Dic47C22⋊C411yescharacteristic
109C2×C4×D47—21no—
110C2×C4×D47—21no—
111C2×C4×D47—21no—
112C2×C4×D47—21no—
113C2×C4×D47—21no—
114C2×C4×D47—21no—
115C2×C4×D47—21no—
116C2×C4×D47—21no—
117C2×C4×D47—22no—
118C2×C4×D47—21no—
119C2×C4×D47—21no—
120C2×C4×D47—41no—
121C2×C4×D47C2×C812yes—
122C2×C4×D47M1612yes—
123C2×C4×D47D812yes—
124C2×C4×D47SD1612yes—
125C2×C8×C47—22no—
126C2×C8×C47—22no—
127C2×C8×C47—41no—
128C2×C8×C47—41no—
129C2×C8×C47—41no—
130C2×C8×C47—41no—
131C4⋊C4×C47—21no—
132C4⋊C4×C47—21no—
133C22⋊C4×C47—41no—
134C22⋊C4×C47—41no—
135C42×C47C2×D411yescharacteristic
136C42×C47C2×D411yescharacteristic
137C42×C47#4111yescharacteristic
138C42×C47#4111yescharacteristic
139C22⋊Dic47—24no—
140C22⋊Dic47—42no—
141C22⋊Dic47—42no—
142(C2×D47)⋊C4—42no—
143C4⋊Dic47—21no—
144C4⋊Dic47—21no—
145C4⋊Dic47—21no—
146C4⋊Dic47C2×C812yescomplemented
147Dic47⋊C4—42no—
148C4×Dic47—21no—
149C4×Dic47—21no—
150C4×Dic47—21no—
151C4×Dic47—21no—
152C4×Dic47—21no—
153C4×Dic47—21no—
154C4×Dic47—41no—
155C4×Dic47—41no—
156C2×C47⋊C8—22no—
157C2×C47⋊C8—22no—
158C2×C47⋊C8—41no—
159C2×C47⋊C8—41no—
160C2×C47⋊C8—41no—
161C2×C47⋊C8—41no—
162C8×D47—48no—
163C23×C47—22no—
164C23×C47—41no—
165C23×C47—41no—
166C23×C47—41no—
167C23×C47—41no—
168C23×C47—41no—
169C23×C47—41no—
170C23×C47C2×C22⋊C411yescharacteristic
171C22×D47—21no—
172C22×D47—21no—
173C22×D47—21no—
174C22×D47—21no—
175C22×D47C22⋊C812yes—
176C22×D47#10212yes—
177C22×D47#10412yes—
178D4×C47—22no—
179D4×C47—22no—
180D4×C47—41no—
181D4×C47—41no—
182C2×C4×C47—21no—
183C2×C4×C47—21no—
184C2×C4×C47—41no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—81no—
188C2×C4×C47—81no—
189C2×C4×C47—81no—
190C2×C4×C47—81no—
191C2×C4×C47C4×D411yescharacteristic
192C2×C4×C47C4×D411yescharacteristic
193C2×C4×C47#12011yescharacteristic
194C2×C4×C47#12111yescharacteristic
195C2×C4×C47#12111yescharacteristic
196C2×C4×C47#12311yescharacteristic
197C2×C4×C47C22×C811yescharacteristic
198C2×C4×C47C2×M1611yescharacteristic
199C2×C4×C47#13111yescharacteristic
200C2×C4×C47#13111yescharacteristic
201C2×C4×C47C2×D811yescharacteristic
202C2×C4×C47C2×SD1611yescharacteristic
203C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C47#13711yescharacteristic
205C22⋊D47—48no—
206C2×Dic47—21no—
207C2×Dic47—21no—
208C2×Dic47—21no—
209C2×Dic47—21no—
210C2×Dic47—21no—
211C2×Dic47—22no—
212C2×Dic47—21no—
213C2×Dic47—21no—
214C2×Dic47—41no—
215C2×Dic47—41no—
216C2×Dic47—41no—
217C2×Dic47—41no—
218C2×Dic47—41no—
219C2×Dic47C22⋊C812yes—
220C2×Dic47#10212yes—
221C4×D47—22no—
222C4×D47—22no—
223C4×D47—22no—
224C4×D47—22no—
225C4×D47—22no—
226C4×D47—22no—
227C4×D47—22no—
228C4×D47—22no—
229C4×D47—42no—
230C4×D47—42no—
231C8×C47—42no—
232C8×C47—42no—
233C47⋊C8—42no—
234C47⋊C8—42no—
235#8939—471nomaximal, Sylow
236C22×C47—42no—
237C22×C47—42no—
238C22×C47—42no—
239C22×C47—81no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47—81no—
243C22×C47#38611yescharacteristic
244C22×C47C2×C22⋊C811yescharacteristic
245C22×C47#40811yescharacteristic
246C22×C47C2×#10211yescharacteristic
247C22×C47#41711yescharacteristic
248C22×C47C2×#10411yescharacteristic
249C22×C47#42111yescharacteristic
250C2×D47—22no—
251C2×D47—22no—
252C2×D47—22no—
253C2×D47—22no—
254C2×D47—22no—
255C2×D47—22no—
256C2×D47D4⋊C814yescomplemented
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—81no—
260C4×C47C8×D411yescharacteristic
261C4×C47C8×D411yescharacteristic
262C4×C47#43511yescharacteristic
263C4×C47#43511yescharacteristic
264C4×C47#44711yescharacteristic
265C4×C47#44811yescharacteristic
266C4×C47#48011yescharacteristic
267C4×C47#48111yescharacteristic
268Dic47—22no—
269Dic47—22no—
270Dic47—41no—
271Dic47—42no—
272Dic47—81no—
273C22×C4⋊C8—471no—
274C4×#121—471no—
275C4×C22⋊C8—471no—
276C2×D4⋊C8—471no—
277C2×D4⋊C8D4711yescharacteristic, complemented
278#1279—471no—
279#1279—471no—
280C2×C47—82no—
281C2×C47C2×D4⋊C811yescharacteristic
282C2×C47#147711yescharacteristic
283C2×C47#148011yescharacteristic
284C2×C47#148311yescharacteristic
285C2×C47#186911yescharacteristic
286C2×C47#187111yescharacteristic
287C2×C47#187411yescharacteristic
288D47—24no—
289C23×C8—941no—
290C2×#121—471no—
291C2×C4×D4—941no—
292C2×C4×D4C2×D4711yescharacteristic
293C22×C42—471no—
294C2×C4⋊C8—471no—
295C2×C4⋊C8—942no—
296C2×C4⋊C8—941no—
297C2×C4⋊C8—942no—
298C2×C4⋊C8C2×D4711yescharacteristic
299C2×C22⋊C8—941no—
300C2×C4×C8—471no—
301C2×C4×C8C2×D4711yescharacteristic
302#390—471no—
303#389—471no—
304#388—941no—
305#386—941no—
306#380—471no—
307C4×C4⋊C4—471no—
308C4×C22⋊C4—941no—
309#336—941no—
310D4⋊C8—22no—
311D4⋊C8—942no—
312C47#893911yescharacteristic, complemented, Sylow
313C22×D4—941no—
314C22×D4C4×D4711yescharacteristic
315C23×C4—21no—
316C23×C4—471no—
317C23×C4—471no—
318C23×C4—471no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—944no—
322C22×C8—941no—
323C22×C8—941no—
324C22×C8—1882no—
325C22×C8—1882no—
326#121—474no—
327#121—942no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—1882no—
333C4×D4—1882no—
334C2×C4⋊C4—471no—
335C2×C4⋊C4—471no—
336C2×C4⋊C4—941no—
337C2×C4⋊C4C4×D4711yescharacteristic
338C2×C22⋊C4—21no—
339C2×C22⋊C4—941no—
340C2×C22⋊C4—941no—
341C2×C22⋊C4—941no—
342C2×C22⋊C4—941no—
343C2×C42—471no—
344C2×C42—471no—
345C2×C42—471no—
346C2×C42—941no—
347C2×C42—941no—
348C2×C42—941no—
349C2×C42—941no—
350C2×C42—941no—
351C2×C42C22×D4711yescharacteristic
352C4⋊C8—21no—
353C4⋊C8—472no—
354C4⋊C8—944no—
355C4⋊C8—941no—
356C4⋊C8C22⋊D4712yescomplemented
357C22⋊C8—944no—
358C4×C8—21no—
359C4×C8—21no—
360C4×C8—941no—
361C4×C8—941no—
362#95—941no—
363#95—941no—
364#95—941no—
365C24—21no—
366C24—471no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—944no—
373C2×D4—1882no—
374C2×D4—1882no—
375C2×D4C8×D4712yescomplemented
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—471no—
384C22×C4—471no—
385C22×C4—472no—
386C22×C4—472no—
387C22×C4—472no—
388C22×C4—472no—
389C22×C4—471no—
390C22×C4—942no—
391C22×C4—941no—
392C22×C4—941no—
393C22×C4—941no—
394C22×C4—941no—
395C22×C4—941no—
396C22×C4—941no—
397C22×C4—941no—
398C22×C4—941no—
399C22×C4—941no—
400C22×C4—941no—
401C22×C4—941no—
402C22×C4—941no—
403C22×C4—1881no—
404C22×C4C2×C4×D4711yescharacteristic
405C22×C4D4×D4711yescharacteristic
406C22×C4D4×D4711yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—942no—
414C2×C8—942no—
415C2×C8—1888no—
416C2×C8—1881no—
417C2×C8—1881no—
418C2×C8—1881no—
419C2×C8—1881no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—472no—
423C4⋊C4—941no—
424C4⋊C4—941no—
425C4⋊C4—941no—
426C4⋊C4—1882no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—944no—
430C22⋊C4—1882no—
431C22⋊C4—1882no—
432C22⋊C4—1882no—
433C42—941no—
434C42—941no—
435C42—941no—
436C42—941no—
437C42—941no—
438C42—941no—
439C42—1881no—
440C42—1881no—
441C42#1062535011yescharacteristic
442C42D4×D4711yescharacteristic
443C42#1062535211yescharacteristic
444C42C2×C22⋊D4711yescharacteristic
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—472no—
453C23—472no—
454C23—472no—
455C23—941no—
456C23—941no—
457C23—941no—
458C23—941no—
459C23C22⋊C4×D4711yescharacteristic
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—1888no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—472no—
475C2×C4—472no—
476C2×C4—941no—
477C2×C4—941no—
478C2×C4—941no—
479C2×C4—941no—
480C2×C4—942no—
481C2×C4—942no—
482C2×C4—942no—
483C2×C4—942no—
484C2×C4—942no—
485C2×C4—942no—
486C2×C4—942no—
487C2×C4—942no—
488C2×C4—941no—
489C2×C4—942no—
490C2×C4—941no—
491C2×C4—941no—
492C2×C4—1882no—
493C2×C4—1882no—
494C2×C4—1881no—
495C2×C4—1881no—
496C2×C4—1881no—
497C2×C4—1881no—
498C2×C4—1881no—
499C2×C4(C22⋊D47)⋊C411yescharacteristic
500C2×C4C4×C22⋊D4711yescharacteristic
501C2×C4#1309399211yescharacteristic
502C2×C4#1309399511yescharacteristic
503C2×C4#1309399711yescharacteristic
504C2×C4#1309400611yescharacteristic
505C2×C4C2×C8×D4711yescharacteristic
506C2×C4M16×D4711yescharacteristic
507C2×C4#1309403011yescharacteristic
508C2×C4#1309403211yescharacteristic
509C2×C4D8×D4711yescharacteristic
510C2×C4SD16×D4711yescharacteristic
511C2×C4#1309404811yescharacteristic
512C2×C4#1309405311yescharacteristic
513C8—42no—
514C8—42no—
515C8—1882no—
516C8—1882no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—474no—
525C22—942no—
526C22—942no—
527C22—942no—
528C22—942no—
529C22—942no—
530C22—942no—
531C22#1568899911yescharacteristic
532C22C22⋊C8×D4711yescharacteristic
533C22#1568908811yescharacteristic
534C22#102×D4711yescharacteristic
535C22#1568912111yescharacteristic
536C22#104×D4711yescharacteristic
537C22#1568913811yescharacteristic
538C4—21no—
539C4—21no—
540C4—81no—
541C4—942no—
542C4—942no—
543C4—3761no—
544C4—1882no—
545C4—1881no—
546C4(C22⋊D47)⋊C811yescharacteristic
547C4C8×C22⋊D4711yescharacteristic
548C4#1568919211yescharacteristic
549C4#1568919711yescharacteristic
550C4#1568925511yescharacteristic
551C4#1568926011yescharacteristic
552C4#1568943511yescharacteristic
553C4#1568944011yescharacteristic
554C2—82no—
555C2—944no—
556C2D4⋊C8×D4711yescharacteristic
557C2#2024177211yescharacteristic
558C2#2024178511yescharacteristic
559C2#2024179811yescharacteristic
560C2#2024367711yescharacteristic
561C2#2024368711yescharacteristic
562C2#2024370211yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×D4⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093995C4
cosocleC2×C42×C47C23
hypercenterC2×D4⋊C8D47
hypocenterC47#8939
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C8×D47C2semidirect
3. C4×(C2×D47)⋊C8C2semidirect
4. C2×D4⋊(C47⋊C8)C2semidirect
5. #20241228C2semidirect
6. #20241227C2semidirect
7. C2×C47×D4⋊C8C2semidirect
41. #13093995C8semidirect
60. C4⋊(C47⋊C8)D4semidirect
80. C4⋊C8×C47D4semidirect
90. C2×D4×C47C2×C8semidirect
146. C4⋊Dic47C2×C8semidirect
256. C2×D47D4⋊C8semidirect
277. C2×D4⋊C8D47semidirect
312. C47#8939semidirect
356. C4⋊C8C22⋊D47semidirect
375. C2×D4C8×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D472
C4×#130939952
C4×(C2×D47)⋊C82
C2×D4⋊(C47⋊C8)2
#202412282
#202412272
C2×C47×D4⋊C82
#893947