Finite Group Databasebeta

← #26187674

Subgroups — #26187674

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252490C211yesmaximal, characteristic
2#20252477C211yesmaximal, characteristic
3#20242297C211yesmaximal, characteristic, complemented
4#20242285C211yesmaximal, characteristic, complemented
5#20242260C211yesmaximal, characteristic, complemented
6#20242260C211yesmaximal, characteristic, complemented
7#20242239C211yesmaximal, characteristic, complemented
8#20242239C211yesmaximal, characteristic, complemented
9#20242207C211yesmaximal, characteristic, complemented
10Q16×C47⋊C8C211yesmaximal, characteristic, complemented
11#20242168C211yesmaximal, characteristic
12#20241861C211yesmaximal, characteristic
13#20241783C211yesmaximal, characteristic
14#20241688C211yesmaximal, characteristic
15C47×#3104C211yesmaximal, characteristic
16#15689254—21no—
17#15689254—21no—
18#15689254—21no—
19#15689254C2211yescharacteristic
20#15689254C2211yescharacteristic
21#15689254C2211yescharacteristic
22#15689254C2211yescharacteristic
23Q8×C47⋊C8—21no—
24Q8×C47⋊C8C2211yescharacteristic
25Q8×C47⋊C8C2211yescharacteristic
26Q8×C47⋊C8C2211yescharacteristic
27Q8×C47⋊C8C2211yescharacteristic
28#15689184—21no—
29#15689184—21no—
30#15689180—21no—
31#15689180C2211yescharacteristic
32#15689176—21no—
33#15689176C2211yescharacteristic
34#15689176C2211yescharacteristic
35#15689176C2211yescharacteristic
36#15688876C2211yescharacteristic
37#15688876C2211yescharacteristic
38#15688874C2211yescharacteristic
39#15688874C2211yescharacteristic
40Q8⋊(C47⋊C8)C2211yescharacteristic
41Q8⋊(C47⋊C8)C2211yescharacteristic
42Q8⋊(C47⋊C8)C2211yescharacteristic
43Q8⋊(C47⋊C8)C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46Q8⋊(C47⋊C8)C2211yescharacteristic
47Q8⋊(C47⋊C8)C2211yescharacteristic
48#15688845C2211yescharacteristic
49#15688845C2211yescharacteristic
50#15688844C2211yescharacteristic
51C8×C47⋊C8C2211yescharacteristic
52C47×#533C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C47×#484C411yescharacteristic
55C47×#484C411yescharacteristic
56C47×#477C411yescharacteristic
57C47×#477C411yescharacteristic
58C47×#462C411yescharacteristic
59C47×#462C411yescharacteristic
60C47×#451C411yescharacteristic
61C47×#451C411yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C4×Q16×C47C2211yescharacteristic
64C4×Q16×C47C2211yescharacteristic
65C4×Q16×C47C2211yescharacteristic
66C47×#431C2211yescharacteristic
67C4⋊(C47⋊C8)—21no—
68C4⋊(C47⋊C8)—21no—
69C4⋊(C47⋊C8)—21no—
70C4⋊(C47⋊C8)—21no—
71C4⋊(C47⋊C8)—21no—
72C4⋊(C47⋊C8)—21no—
73C4⋊(C47⋊C8)—21no—
74C4⋊(C47⋊C8)—21no—
75C4⋊(C47⋊C8)—21no—
76C4⋊(C47⋊C8)D411yescharacteristic
77C4⋊(C47⋊C8)D411yescharacteristic
78C4⋊(C47⋊C8)C2311yescharacteristic
79C4⋊(C47⋊C8)C2311yescharacteristic
80C4⋊(C47⋊C8)C2311yescharacteristic
81C4⋊(C47⋊C8)C2311yescharacteristic
82C22⋊(C47⋊C8)—21no—
83C22⋊(C47⋊C8)—21no—
84C22⋊(C47⋊C8)—21no—
85C22⋊(C47⋊C8)D411yescharacteristic
86C22⋊(C47⋊C8)D411yescharacteristic
87#13093935—21no—
88#13093935—21no—
89#13093935—21no—
90#13093935—21no—
91#13093935—21no—
92C4×C47⋊C8—21no—
93C4×C47⋊C8—21no—
94C4×C47⋊C8—21no—
95C4×C47⋊C8—21no—
96C4×C47⋊C8—21no—
97C4×C47⋊C8C2311yescharacteristic
98C4×C47⋊C8C2311yescharacteristic
99C4×C47⋊C8C2311yescharacteristic
100C4×C47⋊C8C2311yescharacteristic
101C22×Q8×C47C2×C411yescharacteristic
102C2×Q16×C47C2×C411yescharacteristic
103C2×Q16×C47C2×C411yescharacteristic
104C2×Q16×C47C2×C411yescharacteristic
105C2×Q16×C47C2×C411yescharacteristic
106C4⋊Q8×C47C2×C411yescharacteristic
107C4⋊Q8×C47C2×C411yescharacteristic
108#125×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47C2×C411yescharacteristic
111C22⋊Q8×C47C2×C411yescharacteristic
112C4×Q8×C47—21no—
113C4×Q8×C47—21no—
114C4×Q8×C47—21no—
115C4×Q8×C47C2×C411yescharacteristic
116C4×Q8×C47C2×C411yescharacteristic
117C4×Q8×C47C2311yescharacteristic
118C4×Q8×C47C2311yescharacteristic
119C4×Q8×C47C2311yescharacteristic
120C4×Q8×C47C2311yescharacteristic
121#117×C47—21no—
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47C2×C411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126#107×C47C2×C411yescharacteristic
127#107×C47C2×C411yescharacteristic
128#107×C47C2×C411yescharacteristic
129#107×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47C2×C411yescharacteristic
132#103×C47C2×C411yescharacteristic
133#103×C47C2×C411yescharacteristic
134#103×C47C2×C411yescharacteristic
135#103×C47C2×C411yescharacteristic
136#103×C47C2×C411yescharacteristic
137#103×C47C2×C411yescharacteristic
138#103×C47C2×C411yescharacteristic
139#103×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141C22⋊C8×C47C2×C411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—22no—
147C2×Q8×C47—41no—
148C2×Q8×C47C22×C411yescharacteristic
149C2×Q8×C47C22×C411yescharacteristic
150C2×Q8×C47C22×C411yescharacteristic
151C2×Q8×C47C22×C411yescharacteristic
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47#4111yescharacteristic
157Q16×C47—22no—
158Q16×C47—22no—
159Q16×C47—41no—
160Q16×C47—41no—
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47C22×C411yescharacteristic
178C4⋊C4×C47C22×C411yescharacteristic
179C4⋊C4×C47C22×C411yescharacteristic
180C4⋊C4×C47C22×C411yescharacteristic
181C22⋊C4×C47—21no—
182C22⋊C4×C47—21no—
183C42×C47—21no—
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47C22×C411yescharacteristic
190C42×C47C2×D411yescharacteristic
191C42×C47#4111yescharacteristic
192C42×C47C2411yescharacteristic
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8C2×D411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203C23×C47C4×D411yescharacteristic
204Q8×C47—21no—
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—42no—
212Q8×C47—42no—
213Q8×C47#13112yes—
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×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—41no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C4×D411yescharacteristic
232C2×C4×C47C23×C411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C8×C47—21no—
236C8×C47—21no—
237C8×C47—21no—
238C8×C47—21no—
239C47⋊C8—21no—
240C47⋊C8—21no—
241C47⋊C8—21no—
242C47⋊C8—21no—
243C47⋊C8—41no—
244C47⋊C8—41no—
245C47⋊C8—41no—
246C47⋊C8—41no—
247C47⋊C8—41no—
248C47⋊C8—41no—
249#18032—471nomaximal, Sylow
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47C2×C4×D411yescharacteristic
254C4×C47—21no—
255C4×C47—22no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47C2×#13111yescharacteristic
267C4×C47#56811yescharacteristic
268C4×C47#57811yescharacteristic
269C4×C47#57811yescharacteristic
270#3104D4711yescharacteristic
271#2986—471no—
272#2984—471no—
273#1593—471no—
274#1591—471no—
275#1587—471no—
276#1587—471no—
277#1584—471no—
278#1584—471no—
279#1579—471no—
280C8×Q16—471no—
281#1572—471no—
282#1497—471no—
283#1479—471no—
284#1454—471no—
285C2×C47—41no—
286C2×C47#293311yescharacteristic
287C2×C47#295011yescharacteristic
288C2×C47#295511yescharacteristic
289#533C2×D4711yescharacteristic
290C2×C4×Q8C2×D4711yescharacteristic
291#484Dic4711yescharacteristic
292#484Dic4711yescharacteristic
293#477Dic4711yescharacteristic
294#477Dic4711yescharacteristic
295#462Dic4711yescharacteristic
296#462Dic4711yescharacteristic
297#451Dic4711yescharacteristic
298#451Dic4711yescharacteristic
299#446—471no—
300#446—471no—
301#446—471no—
302#446—471no—
303#446—941no—
304#446—941no—
305#446—941no—
306C8×Q8—471no—
307C8×Q8—471no—
308C8×Q8—471no—
309C8×Q8—471no—
310C8×Q8—941no—
311C4×Q16C2×D4711yescharacteristic
312C4×Q16C2×D4711yescharacteristic
313C4×Q16C2×D4711yescharacteristic
314C4×Q16C2×D4711yescharacteristic
315#433—941no—
316#433—941no—
317#432—471no—
318#432—941no—
319#431—471no—
320#431—471no—
321#431—471no—
322#431—941no—
323#431C2×D4711yescharacteristic
324#335—471no—
325#335—471no—
326#334—471no—
327#334—471no—
328Q8⋊C8—471no—
329Q8⋊C8—471no—
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8—471no—
333Q8⋊C8—471no—
334Q8⋊C8—471no—
335Q8⋊C8—471no—
336#322—471no—
337#322—471no—
338#322—471no—
339C82—471no—
340C47#1803211yescharacteristic, complemented, Sylow
341C22×Q8C2×Dic4711yescharacteristic
342C2×Q16C2×Dic4711yescharacteristic
343C2×Q16C2×Dic4711yescharacteristic
344C2×Q16C2×Dic4711yescharacteristic
345C2×Q16C2×Dic4711yescharacteristic
346C4⋊Q8C2×Dic4711yescharacteristic
347C4⋊Q8C2×Dic4711yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C2×Dic4711yescharacteristic
351C22⋊Q8C2×Dic4711yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C2×Dic4711yescharacteristic
356C4×Q8C2×Dic4711yescharacteristic
357C4×Q8C22×D4711yescharacteristic
358C4×Q8C22×D4711yescharacteristic
359C4×Q8C22×D4711yescharacteristic
360C4×Q8C22×D4711yescharacteristic
361#117—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C2×Dic4711yescharacteristic
364C2×C42—21no—
365C2×C42C22×D4711yescharacteristic
366#107C2×Dic4711yescharacteristic
367#107C2×Dic4711yescharacteristic
368#107C2×Dic4711yescharacteristic
369#107C2×Dic4711yescharacteristic
370C4⋊C8—471no—
371C4⋊C8—471no—
372C4⋊C8—471no—
373C4⋊C8—471no—
374C4⋊C8—471no—
375C4⋊C8—471no—
376C4⋊C8—941no—
377C4⋊C8—941no—
378C4⋊C8—941no—
379C4⋊C8—941no—
380C4⋊C8—941no—
381C4⋊C8—941no—
382C4⋊C8—941no—
383C4⋊C8—941no—
384C4⋊C8—941no—
385C4⋊C8C2×Dic4711yescharacteristic
386C4⋊C8C2×Dic4711yescharacteristic
387#103C2×Dic4711yescharacteristic
388#103C2×Dic4711yescharacteristic
389#103C2×Dic4711yescharacteristic
390#103C2×Dic4711yescharacteristic
391#103C2×Dic4711yescharacteristic
392#103C2×Dic4711yescharacteristic
393#103C2×Dic4711yescharacteristic
394#103C2×Dic4711yescharacteristic
395C22⋊C8—471no—
396C22⋊C8—471no—
397C22⋊C8—941no—
398C22⋊C8—941no—
399C22⋊C8—941no—
400C22⋊C8C2×Dic4711yescharacteristic
401C22⋊C8C2×Dic4711yescharacteristic
402#97—941no—
403#97—941no—
404#97—941no—
405#97—941no—
406#97—941no—
407C4×C8—471no—
408C4×C8—471no—
409C4×C8—471no—
410C4×C8—471no—
411C4×C8—941no—
412C4×C8—941no—
413C4×C8—941no—
414C4×C8—941no—
415C4×C8—941no—
416C4×C8C22×D4711yescharacteristic
417C4×C8C22×D4711yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—41no—
422C2×Q8C22×Dic4711yescharacteristic
423C2×Q8C22×Dic4711yescharacteristic
424C2×Q8C22×Dic4711yescharacteristic
425C2×Q8C22×Dic4711yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4D4×D4711yescharacteristic
429C22×C4#1062535211yescharacteristic
430C22×C4C22×Dic4711yescharacteristic
431Q16—22no—
432Q16—22no—
433Q16—41no—
434Q16—41no—
435C2×C8—471no—
436C2×C8—471no—
437C2×C8—471no—
438C2×C8—471no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8C22×Dic4711yescharacteristic
446C2×C8C22×Dic4711yescharacteristic
447C2×C8C22×Dic4711yescharacteristic
448C2×C8C22×Dic4711yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4C22×Dic4711yescharacteristic
462C4⋊C4C22×Dic4711yescharacteristic
463C4⋊C4C22×Dic4711yescharacteristic
464C4⋊C4C22×Dic4711yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42D4×D4711yescharacteristic
474C42#1062535211yescharacteristic
475C42C22×Dic4711yescharacteristic
476C42C23×D4711yescharacteristic
477C23D4×Dic4711yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—42no—
486Q8—42no—
487Q8#1309403112yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4D4×Dic4711yescharacteristic
504C2×C4D4×Dic4711yescharacteristic
505C2×C4D4×Dic4711yescharacteristic
506C2×C4C23×Dic4711yescharacteristic
507C2×C4C2×D4×D4711yescharacteristic
508C2×C4C2×#1062535211yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—941no—
514C8—941no—
515C8—941no—
516C8—941no—
517C8—1881no—
518C8—1881no—
519C8—1881no—
520C8—1881no—
521C8—1881no—
522C8—1881no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×D4×Dic4711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4C2×#1309403111yescharacteristic
540C4#1568989011yescharacteristic
541C4#1568993611yescharacteristic
542C4#1568993611yescharacteristic
543C2—41no—
544C2#2025211511yescharacteristic
545C2#2025225611yescharacteristic
546C2#2025229111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#3104C2
socleC22×C47C2×C4×D4
prime radicalC23×C47C4×D4
cosocleC42×C47C24
hypercenter#3104D47
hypocenterC47#18032
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
3. #20242297C2semidirect
4. #20242285C2semidirect
5. #20242260C2semidirect
6. #20242260C2semidirect
7. #20242239C2semidirect
8. #20242239C2semidirect
9. #20242207C2semidirect
10. Q16×C47⋊C8C2semidirect
340. C47#18032semidirect

Maximal subgroups

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

subgroupindex
#202524902
#202524772
#202422972
#202422852
#202422602
#202422392
#202422072
Q16×C47⋊C82
#202421682
#202418612
#202417832
#202416882
C47×#31042
#1803247