Finite Group Databasebeta

← #26110796

Subgroups — #26110796

Order 12032.

684 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D47C211yesmaximal, characteristic
2C4×#13094000C211yesmaximal, characteristic
3C4×(C2×D47)⋊C8C211yesmaximal, characteristic
4C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5#20241228C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×C8×D47—21no—
9C2×#13094000C411yescharacteristic
10C2×C42×D47C2211yescharacteristic
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×Dic47⋊C8—21no—
13C4⋊C8×D47—22no—
14C4⋊C8×D47—22no—
15C2×(C2×D47)⋊C8—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17#15689030C411yescharacteristic
18#15689019C411yescharacteristic
19#15689004—21no—
20#15688994—21no—
21#15688980C411yescharacteristic
22C4×Dic47⋊C4—21no—
23C4×C4⋊Dic47C2211yescharacteristic
24C4×(C2×D47)⋊C4—21no—
25#15688877—21no—
26Q8⋊(C47⋊C8)—22no—
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C47×Q8⋊C8—22no—
31C22×C4×D47C2×C411yescharacteristic
32C22×C4×D47D411yescharacteristic
33C22×C4×D47D411yescharacteristic
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C2×C8×D47—24no—
37C2×C8×D47—42no—
38C2×C8×D47—42no—
39#13094000—22no—
40#13094000C814yescomplemented
41C2×C4⋊Dic47C2×C411yescharacteristic
42C2×C4⋊Dic47C2×C411yescharacteristic
43C2×Dic47⋊C4—21no—
44C2×Dic47⋊C4—21no—
45C2×(C2×D47)⋊C4—21no—
46C2×(C2×D47)⋊C4—21no—
47C2×C4×Dic47—21no—
48C2×C4×Dic47C2×C411yescharacteristic
49C2×C4×Dic47D411yescharacteristic
50C2×C4×Dic47D411yescharacteristic
51C42×D47—21no—
52C42×D47—21no—
53C42×D47—21no—
54C42×D47—21no—
55C4⋊(C47⋊C8)—21no—
56C4⋊(C47⋊C8)D412yes—
57Dic47⋊C8—24no—
58(C2×D47)⋊C8—24no—
59C4×C47⋊C8—21no—
60C4×C47⋊C8—21no—
61C47⋊#95—21no—
62C47⋊#95—21no—
63C47⋊#95—21no—
64C47⋊#95—21no—
65C47⋊#95—21no—
66C22×Q8×C47C2×C411yescharacteristic
67C22×C8×C47—21no—
68C22×C8×C47—21no—
69C4×Q8×C47—21no—
70C4×Q8×C47—21no—
71C4×Q8×C47—21no—
72C4×Q8×C47—21no—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47C2×C411yescharacteristic
75C2×C42×C47—21no—
76C2×C42×C47C2311yescharacteristic
77C4⋊C8×C47—21no—
78C4⋊C8×C47D412yes—
79C4×C8×C47—21no—
80C4×C8×C47—21no—
81C23×D47C22⋊C411yescharacteristic
82C2×Q8×C47—21no—
83C2×Q8×C47—21no—
84C2×Q8×C47—21no—
85C2×Q8×C47—21no—
86C2×Q8×C47—21no—
87C2×Q8×C47C2×C812yescomplemented
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47C22×C411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C22×Dic47—21no—
94C22×Dic47—21no—
95C22×Dic47C22⋊C411yescharacteristic
96C22×Dic47C22⋊C411yescharacteristic
97C22×Dic47C22⋊C411yescharacteristic
98C2×C4×D47—21no—
99C2×C4×D47—21no—
100C2×C4×D47—21no—
101C2×C4×D47—21no—
102C2×C4×D47—21no—
103C2×C4×D47—21no—
104C2×C4×D47—21no—
105C2×C4×D47—21no—
106C2×C4×D47—22no—
107C2×C4×D47—21no—
108C2×C4×D47—21no—
109C2×C4×D47—41no—
110C2×C4×D47C2×C812yes—
111C2×C4×D47M1612yes—
112C2×C4×D47SD1612yes—
113C2×C4×D47Q1612yes—
114C2×C8×C47—22no—
115C2×C8×C47—22no—
116C2×C8×C47—41no—
117C2×C8×C47—41no—
118C2×C8×C47—41no—
119C2×C8×C47—41no—
120C4⋊C4×C47—21no—
121C4⋊C4×C47—21no—
122C4⋊C4×C47—41no—
123C4⋊C4×C47—41no—
124C42×C47—41no—
125C42×C47—41no—
126C42×C47C2×D411yescharacteristic
127C42×C47C2×D411yescharacteristic
128C42×C47#4111yescharacteristic
129C42×C47#4111yescharacteristic
130(C2×D47)⋊C4—24no—
131(C2×D47)⋊C4—42no—
132C4⋊Dic47—21no—
133C4⋊Dic47—21no—
134C4⋊Dic47—21no—
135C4⋊Dic47C2×C812yescomplemented
136Dic47⋊C4—24no—
137Dic47⋊C4—42no—
138C4×Dic47—21no—
139C4×Dic47—21no—
140C4×Dic47—21no—
141C4×Dic47—21no—
142C4×Dic47—21no—
143C4×Dic47—21no—
144C4×Dic47—41no—
145C4×Dic47—41no—
146C2×C47⋊C8—22no—
147C2×C47⋊C8—22no—
148C2×C47⋊C8—41no—
149C2×C47⋊C8—41no—
150C2×C47⋊C8—41no—
151C2×C47⋊C8—41no—
152C8×D47—48no—
153C23×C47C2×C22⋊C411yescharacteristic
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47—21no—
158C22×D47C22⋊C812yes—
159C22×D47#10312yes—
160C22×D47#10412yes—
161Q8×C47—22no—
162Q8×C47—22no—
163Q8×C47—41no—
164Q8×C47—41no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—22no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47C4×D411yescharacteristic
174C2×C4×C47C4×D411yescharacteristic
175C2×C4×C47#12011yescharacteristic
176C2×C4×C47#12111yescharacteristic
177C2×C4×C47#12111yescharacteristic
178C2×C4×C47#12311yescharacteristic
179C2×C4×C47C22×C811yescharacteristic
180C2×C4×C47C2×M1611yescharacteristic
181C2×C4×C47#13111yescharacteristic
182C2×C4×C47#13111yescharacteristic
183C2×C4×C47C2×SD1611yescharacteristic
184C2×C4×C47C2×Q1611yescharacteristic
185C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C47#13711yescharacteristic
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47—21no—
191C2×Dic47—21no—
192C2×Dic47—22no—
193C2×Dic47—21no—
194C2×Dic47—21no—
195C2×Dic47—41no—
196C2×Dic47—41no—
197C2×Dic47—41no—
198C2×Dic47—41no—
199C2×Dic47—41no—
200C2×Dic47C22⋊C812yes—
201C2×Dic47#10312yes—
202C4×D47—22no—
203C4×D47—22no—
204C4×D47—22no—
205C4×D47—22no—
206C4×D47—22no—
207C4×D47—22no—
208C4×D47—22no—
209C4×D47—22no—
210C4×D47—42no—
211C4×D47—42no—
212C8×C47—42no—
213C8×C47—42no—
214C47⋊C8—42no—
215C47⋊C8—42no—
216#8937—471nomaximal, Sylow
217C22×C47#38611yescharacteristic
218C22×C47C2×C22⋊C811yescharacteristic
219C22×C47#40811yescharacteristic
220C22×C47C2×#10311yescharacteristic
221C22×C47#41711yescharacteristic
222C22×C47C2×#10411yescharacteristic
223C22×C47#42111yescharacteristic
224C2×D47—22no—
225C2×D47—22no—
226C2×D47—22no—
227C2×D47—22no—
228C2×D47—22no—
229C2×D47—22no—
230C2×D47Q8⋊C814yescomplemented
231C4×C47—21no—
232C4×C47—21no—
233C4×C47—42no—
234C4×C47—81no—
235C4×C47C8×D411yescharacteristic
236C4×C47C8×D411yescharacteristic
237C4×C47#43511yescharacteristic
238C4×C47#43511yescharacteristic
239C4×C47#45011yescharacteristic
240C4×C47#45111yescharacteristic
241C4×C47#48311yescharacteristic
242C4×C47#48411yescharacteristic
243Dic47—22no—
244Dic47—22no—
245Dic47—41no—
246Dic47—42no—
247Dic47—81no—
248C22×C4⋊C8—471no—
249C4×C22⋊Q8—471no—
250C4×C22⋊C8—471no—
251C2×Q8⋊C8—471no—
252C2×Q8⋊C8D4711yescharacteristic, complemented
253#1279—471no—
254#1279—471no—
255C2×C47C2×Q8⋊C811yescharacteristic
256C2×C47#147711yescharacteristic
257C2×C47#148111yescharacteristic
258C2×C47#148311yescharacteristic
259C2×C47#186911yescharacteristic
260C2×C47#187111yescharacteristic
261C2×C47#187211yescharacteristic
262D47—24no—
263C23×C8—941no—
264C2×C22⋊Q8—471no—
265C2×C4×Q8C2×D4711yescharacteristic
266C22×C42—471no—
267C2×C4⋊C8—471no—
268C2×C4⋊C8—942no—
269C2×C4⋊C8—941no—
270C2×C4⋊C8—942no—
271C2×C4⋊C8C2×D4711yescharacteristic
272C2×C22⋊C8—941no—
273C2×C4×C8—471no—
274C2×C4×C8C2×D4711yescharacteristic
275#391—471no—
276#389—471no—
277#387—941no—
278#385—941no—
279#380—471no—
280C4×C4⋊C4—471no—
281C4×C4⋊C4—941no—
282C4×C22⋊C4—941no—
283#336—941no—
284Q8⋊C8—22no—
285Q8⋊C8—942no—
286C47#893711yescharacteristic, complemented, Sylow
287C22×Q8C4×D4711yescharacteristic
288C23×C4—471no—
289C23×C4—471no—
290C23×C4—471no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—944no—
294C22×C8—941no—
295C22×C8—941no—
296C22×C8—1882no—
297C22×C8—1882no—
298C22⋊Q8—474no—
299C22⋊Q8—942no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—471no—
306C2×C4⋊C4—471no—
307C2×C4⋊C4—941no—
308C2×C4⋊C4—941no—
309C2×C4⋊C4C4×D4711yescharacteristic
310C2×C22⋊C4—941no—
311C2×C22⋊C4—941no—
312C2×C42—21no—
313C2×C42—471no—
314C2×C42—471no—
315C2×C42—471no—
316C2×C42—941no—
317C2×C42—941no—
318C2×C42—941no—
319C2×C42—941no—
320C2×C42—941no—
321C2×C42C22×D4711yescharacteristic
322C4⋊C8—21no—
323C4⋊C8—472no—
324C4⋊C8—944no—
325C4⋊C8—941no—
326C4⋊C8C22⋊D4712yes—
327C22⋊C8—944no—
328C4×C8—21no—
329C4×C8—21no—
330C4×C8—941no—
331C4×C8—941no—
332#95—941no—
333#95—941no—
334#95—941no—
335#95—941no—
336#95—941no—
337C24—471no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C8×D4712yescomplemented
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—471no—
347C22×C4—471no—
348C22×C4—472no—
349C22×C4—472no—
350C22×C4—472no—
351C22×C4—472no—
352C22×C4—471no—
353C22×C4—942no—
354C22×C4—941no—
355C22×C4—941no—
356C22×C4—941no—
357C22×C4—941no—
358C22×C4—941no—
359C22×C4—941no—
360C22×C4—941no—
361C22×C4—941no—
362C22×C4—941no—
363C22×C4—941no—
364C22×C4—941no—
365C22×C4—941no—
366C22×C4—1881no—
367C22×C4C2×C4×D4711yescharacteristic
368C22×C4D4×D4711yescharacteristic
369C22×C4D4×D4711yescharacteristic
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—942no—
377C2×C8—942no—
378C2×C8—1888no—
379C2×C8—1881no—
380C2×C8—1881no—
381C2×C8—1881no—
382C2×C8—1881no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—472no—
388C4⋊C4—944no—
389C4⋊C4—941no—
390C4⋊C4—941no—
391C4⋊C4—941no—
392C4⋊C4—1882no—
393C22⋊C4—944no—
394C22⋊C4—1882no—
395C42—41no—
396C42—41no—
397C42—941no—
398C42—941no—
399C42—941no—
400C42—941no—
401C42—941no—
402C42—941no—
403C42—1881no—
404C42—1881no—
405C42#1062535011yescharacteristic
406C42D4×D4711yescharacteristic
407C42#1062535211yescharacteristic
408C42C2×C22⋊D4711yescharacteristic
409C23—472no—
410C23—472no—
411C23—472no—
412C23—941no—
413C23—941no—
414C23—941no—
415C23—941no—
416C23C22⋊C4×D4711yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—41no—
420Q8—41no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—472no—
430C2×C4—472no—
431C2×C4—941no—
432C2×C4—941no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—942no—
436C2×C4—942no—
437C2×C4—942no—
438C2×C4—942no—
439C2×C4—942no—
440C2×C4—942no—
441C2×C4—942no—
442C2×C4—942no—
443C2×C4—941no—
444C2×C4—942no—
445C2×C4—941no—
446C2×C4—941no—
447C2×C4—1882no—
448C2×C4—1882no—
449C2×C4—1881no—
450C2×C4—1881no—
451C2×C4—1881no—
452C2×C4—1881no—
453C2×C4—1881no—
454C2×C4(C22⋊D47)⋊C411yescharacteristic
455C2×C4C4×C22⋊D4711yescharacteristic
456C2×C4#1309399211yescharacteristic
457C2×C4#1309399511yescharacteristic
458C2×C4#1309399711yescharacteristic
459C2×C4#1309400611yescharacteristic
460C2×C4C2×C8×D4711yescharacteristic
461C2×C4M16×D4711yescharacteristic
462C2×C4#1309403011yescharacteristic
463C2×C4#1309403211yescharacteristic
464C2×C4SD16×D4711yescharacteristic
465C2×C4Q16×D4711yescharacteristic
466C2×C4#1309405111yescharacteristic
467C2×C4#1309405611yescharacteristic
468C8—42no—
469C8—42no—
470C8—1882no—
471C8—1882no—
472C22—474no—
473C22—942no—
474C22—942no—
475C22—942no—
476C22—942no—
477C22—942no—
478C22—942no—
479C22#1568899911yescharacteristic
480C22C22⋊C8×D4711yescharacteristic
481C22#1568908811yescharacteristic
482C22#103×D4711yescharacteristic
483C22#1568912311yescharacteristic
484C22#104×D4711yescharacteristic
485C22#1568913811yescharacteristic
486C4—21no—
487C4—21no—
488C4—42no—
489C4—81no—
490C4—942no—
491C4—942no—
492C4—3761no—
493C4—1882no—
494C4—1881no—
495C4(C22⋊D47)⋊C811yescharacteristic
496C4C8×C22⋊D4711yescharacteristic
497C4#1568919211yescharacteristic
498C4#1568919711yescharacteristic
499C4#1568927211yescharacteristic
500C4#1568927711yescharacteristic
501C4#1568945211yescharacteristic
502C4#1568945711yescharacteristic
503C2—944no—
504C2Q8⋊C8×D4711yescharacteristic
505C2#2024177411yescharacteristic
506C2#2024178911yescharacteristic
507C2#2024180011yescharacteristic
508C2#2024367711yescharacteristic
509C2#2024368711yescharacteristic
510C2#2024369211yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47#8937
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊(C47⋊C8)C2semidirect
5. #20241228C2semidirect
6. #20241227C2semidirect
7. C2×C47×Q8⋊C8C2semidirect
40. #13094000C8semidirect
87. C2×Q8×C47C2×C8semidirect
135. C4⋊Dic47C2×C8semidirect
230. C2×D47Q8⋊C8semidirect
252. C2×Q8⋊C8D47semidirect
286. C47#8937semidirect
343. C2×Q8C8×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×#130940002
C4×(C2×D47)⋊C82
C2×Q8⋊(C47⋊C8)2
#202412282
#202412272
C2×C47×Q8⋊C82
#893747