Finite Group Databasebeta

← #26186927

Subgroups — #26186927

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253994C211yesmaximal, characteristic
2#20252539C211yesmaximal, characteristic
3#20252482C211yesmaximal, characteristic, complemented
4#20242298C211yesmaximal, characteristic, complemented
5#20242292C211yesmaximal, characteristic, complemented
6#20242286C211yesmaximal, characteristic, complemented
7#20242280C211yesmaximal, characteristic, complemented
8#20242208C211yesmaximal, characteristic, complemented
9#20242202C211yesmaximal, characteristic, complemented
10C8×Dic188C211yesmaximal, characteristic, complemented
11C8×#10625325C211yesmaximal, characteristic, complemented
12#20242155C211yesmaximal, characteristic, complemented
13#20241849C211yesmaximal, characteristic
14#20241844C211yesmaximal, characteristic, complemented
15C8×M16×C47C211yesmaximal, characteristic, complemented
16#15689680C2211yescharacteristic
17#15689657C2211yescharacteristic
18#15689532C411yescharacteristic
19#15689517C411yescharacteristic
20#15689492C411yescharacteristic
21#15689483C411yescharacteristic
22#15689381C411yescharacteristic
23#15689381C411yescharacteristic
24#15689369C411yescharacteristic
25#15689369C411yescharacteristic
26#15689253C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689253C2211yescharacteristic
29#15689252—21no—
30#15689252—21no—
31C8×Dic94C2211yescharacteristic
32C8×Dic94C2211yescharacteristic
33C8×Dic94C2211yescharacteristic
34C4×Dic188C2211yescharacteristic
35C4×Dic188C2211yescharacteristic
36C4×#10625325C2211yescharacteristic
37C4×#10625325C2211yescharacteristic
38#15689202C2211yescharacteristic
39#15689198—21no—
40#15689197—21no—
41C8×D188C2211yescharacteristic
42#15689183—21no—
43#15689181—21no—
44#15689181—21no—
45#15689180C2211yescharacteristic
46#15689148—21no—
47#15689147C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688874C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688855C2211yescharacteristic
57#15688855C2211yescharacteristic
58#15688852C2211yescharacteristic
59#15688852C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C4×M16×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C82×C47C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×Dic188C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625324—21no—
73C2×C8×D47—21no—
74#13094024C2×C411yescharacteristic
75#13094024C2×C411yescharacteristic
76#13094018—21no—
77#13094016—21no—
78#13094016C2×C411yescharacteristic
79#13094012C2×C411yescharacteristic
80#13094007—21no—
81#13094003—21no—
82#13094003C2×C411yescharacteristic
83#13094003C2×C411yescharacteristic
84#13094003C2×C411yescharacteristic
85#13093998C2×C411yescharacteristic
86C4×Dic94—21no—
87C4×Dic94C2311yescharacteristic
88C4×Dic94C2311yescharacteristic
89C4×Dic94C2311yescharacteristic
90C4×D188C2311yescharacteristic
91C4×C22⋊D47—21no—
92#13093983—21no—
93#13093981—21no—
94#13093958C2×C411yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093956C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093949C2×C411yescharacteristic
112#13093949C2×C411yescharacteristic
113#13093949C2×C411yescharacteristic
114#13093949C2×C411yescharacteristic
115#13093946C2×C411yescharacteristic
116#13093946C2×C411yescharacteristic
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120#13093935—21no—
121#13093934—21no—
122#13093934—21no—
123#13093934—21no—
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C2×M16×C47C2×C411yescharacteristic
128C2×M16×C47C2×C411yescharacteristic
129C22×C8×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47D411yescharacteristic
133C22⋊C8×C47D411yescharacteristic
134C22⋊C8×C47D411yescharacteristic
135#97×C47C2×C411yescharacteristic
136#97×C47C2×C411yescharacteristic
137C4×C8×C47—21no—
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148C2×D188C22×C411yescharacteristic
149C2×C4×D47—21no—
150C2×Dic94—21no—
151C2×Dic94C22×C411yescharacteristic
152C2×Dic94C22×C411yescharacteristic
153C2×Dic94C22×C411yescharacteristic
154M16×C47—22no—
155M16×C47—22no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—42no—
159C2×C8×C47C22×C411yescharacteristic
160C2×C8×C47C22×C411yescharacteristic
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C42×C47C22×C411yescharacteristic
168C42×C47C2×D411yescharacteristic
169C42×C47#4111yescharacteristic
170C42×C47C2411yescharacteristic
171C22⋊Dic47—21no—
172C22⋊Dic47—21no—
173C22⋊Dic47—21no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176(C2×D47)⋊C4—21no—
177(C2×D47)⋊C4—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47C22×C411yescharacteristic
182C4⋊Dic47C22×C411yescharacteristic
183C4⋊Dic47C22×C411yescharacteristic
184C4⋊Dic47C22×C411yescharacteristic
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196#10625329—81no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201Dic188—22no—
202Dic188—22no—
203#10625325—22no—
204#10625325—22no—
205#10625324—81no—
206C8×D47—81no—
207C23×C47C4×D411yescharacteristic
208C22×D47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—41no—
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C23×C411yescharacteristic
218C2×C4×C47C22×D411yescharacteristic
219C2×C4×C47C2×#4111yescharacteristic
220C22⋊D47—81no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47—21no—
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228D188—21no—
229D188—21no—
230C4×D47—41no—
231C4×D47—41no—
232Dic94—21no—
233Dic94—21no—
234Dic94—21no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—81no—
239C8×C47—22no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—41no—
247C8×C47#13112yes—
248C8×C47#13112yes—
249C47⋊C8—41no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253#17969—471nomaximal, Sylow
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47C2×C4×D411yescharacteristic
258C2×D47—41no—
259C2×D47—41no—
260C2×D47—41no—
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47C2×#13111yescharacteristic
266C4×C47C2×#13111yescharacteristic
267C4×C47#57711yescharacteristic
268C4×C47#57811yescharacteristic
269Dic47—41no—
270Dic47—41no—
271Dic47—41no—
272Dic47—41no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276#3172—471no—
277#2993—471no—
278#2985—471no—
279#1593—471no—
280#1592—471no—
281#1591—471no—
282#1590—471no—
283#1579—471no—
284SD16⋊C8—471no—
285C8×Q16—471no—
286C8×SD16—471no—
287#1569—471no—
288#1494—471no—
289#1493—471no—
290C8×M16D4711yescharacteristic, complemented
291C2×C47—41no—
292C2×C47#293111yescharacteristic
293C2×C47#294711yescharacteristic
294C2×C47#295611yescharacteristic
295D47—81no—
296#533—471no—
297#529—471no—
298#501—471no—
299#497—471no—
300#491—471no—
301#489—471no—
302#470—471no—
303#470—471no—
304#468—471no—
305#468—471no—
306#446—471no—
307#446—471no—
308#446—471no—
309#446—941no—
310#446—941no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—471no—
314C4×Q16—471no—
315C4×Q16—471no—
316C4×SD16—471no—
317C4×SD16—471no—
318#436—471no—
319#436—941no—
320#435—941no—
321C8×D4—471no—
322#433—941no—
323#433—941no—
324#433—941no—
325#432—471no—
326#431C2×D4711yescharacteristic
327#424—941no—
328#423—471no—
329C4×M16C2×D4711yescharacteristic
330C2×C4×C8C2×D4711yescharacteristic
331#335—471no—
332#335—471no—
333#334—471no—
334#334—471no—
335Q8⋊C8—471no—
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341D4⋊C8—471no—
342D4⋊C8—471no—
343#322C2×D4711yescharacteristic
344#322C2×D4711yescharacteristic
345C82C2×D4711yescharacteristic
346C82C2×D4711yescharacteristic
347C47#1796911yescharacteristic, complemented, Sylow
348C2×Q16—471no—
349C2×Q16—471no—
350C2×SD16—471no—
351C2×SD16—471no—
352C2×M16—941no—
353C2×M16—941no—
354C2×M16C4×D4711yescharacteristic
355C2×M16C4×D4711yescharacteristic
356C22×C8—21no—
357C22×C8—941no—
358C4⋊Q8—471no—
359C4⋊Q8—471no—
360#126—941no—
361#125—471no—
362#125—941no—
363#124—471no—
364#123—941no—
365C22⋊Q8—471no—
366C22⋊Q8—471no—
367C22⋊Q8—471no—
368C22⋊Q8—941no—
369#121—471no—
370C4×Q8—471no—
371C4×Q8—471no—
372C4×Q8—471no—
373C4×Q8—941no—
374C4×D4—471no—
375C4×D4—941no—
376#117—941no—
377#117—941no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—471no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8D18811yescharacteristic
395C4⋊C8D18811yescharacteristic
396#103—471no—
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#102—471no—
403#102—471no—
404C22⋊C8—941no—
405C22⋊C8—941no—
406C22⋊C8—941no—
407C22⋊C8D18811yescharacteristic
408C22⋊C8D18811yescharacteristic
409#97—941no—
410#97—941no—
411#97—941no—
412#97—941no—
413#97C4×D4711yescharacteristic
414#97C4×D4711yescharacteristic
415C4×C8—21no—
416C4×C8—941no—
417C4×C8—941no—
418C4×C8—941no—
419C4×C8C22×D4711yescharacteristic
420C4×C8C22×D4711yescharacteristic
421C4×C8C22×D4711yescharacteristic
422C4×C8C22×D4711yescharacteristic
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C2×Q8—471no—
426C2×Q8—471no—
427C2×Q8—471no—
428C2×Q8—941no—
429C2×D4—471no—
430C2×D4—941no—
431C22×C4—941no—
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4C2×D18811yescharacteristic
434C22×C4#1062535011yescharacteristic
435Q16—942no—
436Q16—942no—
437SD16—942no—
438SD16—942no—
439M16—22no—
440M16—22no—
441M16—3761no—
442M16—3761no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C2×C8—941no—
450C2×C8—3761no—
451C2×C8C2×C4×D4711yescharacteristic
452C2×C8C2×C4×D4711yescharacteristic
453C2×C8C2×C4×D4711yescharacteristic
454C2×C8C2×C4×D4711yescharacteristic
455C2×C8C2×D18811yescharacteristic
456C2×C8C2×D18811yescharacteristic
457C2×C8C2×D18811yescharacteristic
458C2×C8C2×D18811yescharacteristic
459C4⋊C4—471no—
460C4⋊C4—471no—
461C4⋊C4—471no—
462C4⋊C4—471no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C22⋊C4—941no—
475C22⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42C2×D18811yescharacteristic
486C42#1062535011yescharacteristic
487C42C23×D4711yescharacteristic
488C23—941no—
489C23C4×D18811yescharacteristic
490Q8—941no—
491Q8—941no—
492Q8—941no—
493Q8—941no—
494Q8—941no—
495Q8—941no—
496Q8—3761no—
497D4—941no—
498D4—941no—
499D4—3761no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—941no—
506C2×C4—941no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—1881no—
513C2×C4—1881no—
514C2×C4C4×D18811yescharacteristic
515C2×C4C4×D18811yescharacteristic
516C2×C4C4×D18811yescharacteristic
517C2×C4C22×C4×D4711yescharacteristic
518C2×C4C22×D18811yescharacteristic
519C2×C4C2×#1062535011yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—1881no—
529C8—1881no—
530C8—1881no—
531C8—1881no—
532C8#1309403012yes—
533C8#1309403012yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—1881no—
538C22—1881no—
539C22—1881no—
540C22C2×C4×D18811yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—1881no—
546C4—1881no—
547C4—1881no—
548C4—1881no—
549C4—1881no—
550C4—1881no—
551C4—1881no—
552C4C2×#1309403011yescharacteristic
553C4C2×#1309403011yescharacteristic
554C4#1568993511yescharacteristic
555C4#1568994011yescharacteristic
556C2—41no—
557C2—3761no—
558C2#2025210111yescharacteristic
559C2#2025223311yescharacteristic
560C2#2025229911yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC8×M16×C47C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenterC8×M16D47
hypocenterC47#17969
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
3. #20252482C2semidirect
4. #20242298C2semidirect
5. #20242292C2semidirect
6. #20242286C2semidirect
7. #20242280C2semidirect
8. #20242208C2semidirect
9. #20242202C2semidirect
10. C8×Dic188C2semidirect
11. C8×#10625325C2semidirect
12. #20242155C2semidirect
14. #20241844C2semidirect
15. C8×M16×C47C2semidirect
290. C8×M16D47semidirect
347. C47#17969semidirect

Maximal subgroups

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

subgroupindex
#202539942
#202525392
#202524822
#202422982
#202422922
#202422862
#202422802
#202422082
#202422022
C8×Dic1882
C8×#106253252
#202421552
#202418492
#202418442
C8×M16×C472
#1796947