Finite Group Databasebeta

← #26186428

Subgroups — #26186428

Order 12032.

586 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253425C211yesmaximal, characteristic
2#20252479C211yesmaximal, characteristic
3#20252467C211yesmaximal, characteristic
4#20242260C211yesmaximal, characteristic, complemented
5#20242258C211yesmaximal, characteristic, complemented
6#20242241C211yesmaximal, characteristic, complemented
7#20242235C211yesmaximal, characteristic, complemented
8#20242208C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625337C211yesmaximal, characteristic, complemented
11#20242165C211yesmaximal, characteristic
12#20241833C211yesmaximal, characteristic
13#20241807C211yesmaximal, characteristic
14#20241684C211yesmaximal, characteristic
15C47×#1579C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17C4×Q8×D47C2211yescharacteristic
18#15689460C411yescharacteristic
19#15689457C411yescharacteristic
20#15689417C411yescharacteristic
21#15689416C411yescharacteristic
22#15689332C411yescharacteristic
23#15689331C411yescharacteristic
24#15689280C411yescharacteristic
25#15689277C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689253—21no—
28#15689252—21no—
29#15689250C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31C8×Dic94—21no—
32C8×Dic94C2211yescharacteristic
33C8×Dic94C2211yescharacteristic
34#15689247—21no—
35#15689247C2211yescharacteristic
36C4×Dic188C2211yescharacteristic
37C4×#10625337C2211yescharacteristic
38C4×#10625337C2211yescharacteristic
39#15689183—21no—
40#15689182—21no—
41#15689179C2211yescharacteristic
42#15689175—21no—
43#15689175C2211yescharacteristic
44#15689174—21no—
45#15689174C2211yescharacteristic
46#15689174C2211yescharacteristic
47C4×#10625324C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54Q8⋊(C47⋊C8)C2211yescharacteristic
55#15688853C2211yescharacteristic
56#15688853C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688845C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Q8×D47C2×C411yescharacteristic
68C2×Dic188C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625337C2×C411yescharacteristic
71C2×#10625324—21no—
72#13094023C2×C411yescharacteristic
73#13094022C2×C411yescharacteristic
74#13094014—21no—
75#13094004C2×C411yescharacteristic
76#13094002—21no—
77#13094000C2×C411yescharacteristic
78Q8×Dic47C2×C411yescharacteristic
79C4×Dic94—21no—
80C4×Dic94—21no—
81C4×Dic94C2311yescharacteristic
82C4×Dic94C2311yescharacteristic
83#13093989—21no—
84#13093989C2×C411yescharacteristic
85#13093981—21no—
86C4⋊C4×D47—21no—
87C4⋊C4×D47C2×C411yescharacteristic
88C42×D47—21no—
89C42×D47C2311yescharacteristic
90#13093958C2×C411yescharacteristic
91#13093957C2×C411yescharacteristic
92#13093957C2×C411yescharacteristic
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)—21no—
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8C2×C411yescharacteristic
102Dic47⋊C8C2×C411yescharacteristic
103Dic47⋊C8D411yescharacteristic
104Dic47⋊C8D411yescharacteristic
105#13093949C2×C411yescharacteristic
106#13093949C2×C411yescharacteristic
107#13093948C2×C411yescharacteristic
108#13093948C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111(C2×D47)⋊C8—21no—
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8C2×C411yescharacteristic
114(C2×D47)⋊C8C2×C411yescharacteristic
115(C2×D47)⋊C8D411yescharacteristic
116(C2×D47)⋊C8D411yescharacteristic
117#13093935—21no—
118#13093934—21no—
119#13093934—21no—
120#13093934—21no—
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×Q16×C47C2×C411yescharacteristic
130C4×Q8×C47C2311yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132#107×C47C2×C411yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#103×C47C2×C411yescharacteristic
139C4×C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146Q8×D47—22no—
147Q8×D47—22no—
148C2×C4×D47—21no—
149C2×C4×D47—21no—
150C2×C4×D47C22×C411yescharacteristic
151C2×C4×D47C2×D411yescharacteristic
152C2×C4×D47#4111yescharacteristic
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157Q16×C47—22no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47C22×C411yescharacteristic
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C2×D411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47C22×C411yescharacteristic
168C4⋊C4×C47C22×C411yescharacteristic
169C42×C47—21no—
170C42×C47—21no—
171C42×C47C2411yescharacteristic
172#10625337—22no—
173#10625337—22no—
174(C2×D47)⋊C4—21no—
175(C2×D47)⋊C4—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47C22×C411yescharacteristic
179C4⋊Dic47C22×C411yescharacteristic
180Dic47⋊C4—21no—
181Dic47⋊C4—21no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47C22×C411yescharacteristic
193C4×Dic47C2×D411yescharacteristic
194C4×Dic47#4111yescharacteristic
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202Dic188—22no—
203#10625324—42no—
204C22×D47C4×D411yescharacteristic
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208Q8×C47#13112yes—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47C23×C411yescharacteristic
214C2×C4×C47C22×D411yescharacteristic
215C2×C4×C47C2×#4111yescharacteristic
216C2×Dic47—21no—
217C2×Dic47—21no—
218C2×Dic47—21no—
219C2×Dic47—21no—
220C2×Dic47C4×D411yescharacteristic
221C2×Dic47C4×D411yescharacteristic
222C2×Dic47C4×D411yescharacteristic
223C4×D47—24no—
224C4×D47—21no—
225C4×D47—21no—
226C4×D47—21no—
227C4×D47—21no—
228C4×D47—41no—
229C4×D47—81no—
230Dic94—24no—
231Dic94—21no—
232Dic94—21no—
233Dic94—21no—
234Dic94—81no—
235Dic94#13112yes—
236C8×C47—21no—
237C8×C47—21no—
238C8×C47—21no—
239C8×C47—21no—
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C47⋊C8—22no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—41no—
249C47⋊C8—41no—
250#17925—471nomaximal, Sylow
251C22×C47C2×C4×D411yescharacteristic
252C2×D47—21no—
253C2×D47—21no—
254C2×D47—21no—
255C4×C47—22no—
256C4×C47—21no—
257C4×C47—41no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47C2×#13111yescharacteristic
261C4×C47C2×#13111yescharacteristic
262C4×C47#57811yescharacteristic
263C4×C47#57811yescharacteristic
264Dic47—21no—
265Dic47—22no—
266Dic47—21no—
267Dic47—21no—
268Dic47—41no—
269Dic47—41no—
270Dic47—41no—
271#3104—471no—
272#2985—471no—
273#2982—471no—
274#1587—471no—
275#1587—471no—
276#1584—471no—
277#1584—471no—
278#1579—471no—
279#1579D4711yescharacteristic, complemented
280C8×Q16—471no—
281C8×Q16—471no—
282#1572—471no—
283#1491—471no—
284#1485—471no—
285#1453—471no—
286C2×C47#292911yescharacteristic
287C2×C47#295011yescharacteristic
288C2×C47#295611yescharacteristic
289D47—41no—
290#533—471no—
291C2×C4×Q8—471no—
292#484—471no—
293#484—471no—
294#477—471no—
295#477—471no—
296#462—471no—
297#462—471no—
298#451—471no—
299#451—471no—
300#446—471no—
301#446—471no—
302#446—941no—
303#446—941no—
304C8×Q8—471no—
305C8×Q8—471no—
306C8×Q8—471no—
307C8×Q8—471no—
308C8×Q8—941no—
309C8×Q8—941no—
310C8×Q8C2×D4711yescharacteristic
311C8×Q8C2×D4711yescharacteristic
312C4×Q16—471no—
313C4×Q16—471no—
314C4×Q16—471no—
315C4×Q16C2×D4711yescharacteristic
316#433—941no—
317#433—941no—
318#432—471no—
319#431—471no—
320#431—471no—
321#431—471no—
322#431—941no—
323#431—941no—
324C4×M16—471no—
325#335—471no—
326#335—471no—
327#334—471no—
328#334C2×D4711yescharacteristic
329Q8⋊C8—471no—
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8—471no—
333Q8⋊C8—471no—
334Q8⋊C8—471no—
335Q8⋊C8C2×D4711yescharacteristic
336Q8⋊C8C2×D4711yescharacteristic
337#322—471no—
338#322—471no—
339#322C2×D4711yescharacteristic
340C82—471no—
341C47#1792511yescharacteristic, complemented, Sylow
342C22×Q8—471no—
343C2×Q16—471no—
344C2×Q16—471no—
345C2×Q16—471no—
346C2×Q16C4×D4711yescharacteristic
347C2×M16—941no—
348C4⋊Q8—471no—
349C4⋊Q8—471no—
350#125—941no—
351C22⋊Q8—471no—
352C22⋊Q8—471no—
353C22⋊Q8—941no—
354C4×Q8—471no—
355C4×Q8—471no—
356C4×Q8—471no—
357C4×Q8—471no—
358C4×Q8—941no—
359C4×Q8—941no—
360C4×Q8—941no—
361C4×Q8C22×D4711yescharacteristic
362C4×Q8C22×D4711yescharacteristic
363#117—941no—
364C2×C4⋊C4—471no—
365C2×C4⋊C4—941no—
366C2×C42—471no—
367C2×C42—941no—
368#107—471no—
369#107—471no—
370#107—471no—
371#107C4×D4711yescharacteristic
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—471no—
375C4⋊C8—471no—
376C4⋊C8—471no—
377C4⋊C8—471no—
378C4⋊C8—471no—
379C4⋊C8—471no—
380C4⋊C8—941no—
381C4⋊C8—941no—
382C4⋊C8—941no—
383C4⋊C8—941no—
384C4⋊C8—941no—
385C4⋊C8—941no—
386C4⋊C8C22×D4711yescharacteristic
387C4⋊C8C22×D4711yescharacteristic
388#103—471no—
389#103—471no—
390#103—471no—
391#103—471no—
392#103—471no—
393#103—471no—
394#103C4×D4711yescharacteristic
395#103C4×D4711yescharacteristic
396C22⋊C8—471no—
397C22⋊C8—471no—
398C22⋊C8—471no—
399C22⋊C8—471no—
400C22⋊C8—941no—
401C22⋊C8—941no—
402#97—941no—
403#97—941no—
404#97—941no—
405#97—941no—
406C4×C8—21no—
407C4×C8—21no—
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
418C4×C8C22×D4711yescharacteristic
419C2×Q8—471no—
420C2×Q8—471no—
421C2×Q8—941no—
422C2×Q8—941no—
423C2×Q8—942no—
424C2×Q8—942no—
425C2×Q8C2×C4×D4711yescharacteristic
426C2×Q8C2×C4×D4711yescharacteristic
427C22×C4—471no—
428C22×C4—471no—
429C22×C4—471no—
430C22×C4—941no—
431C22×C4—941no—
432Q16—22no—
433Q16—942no—
434Q16—942no—
435Q16—942no—
436M16—1882no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—471no—
441C2×C8—471no—
442C2×C8—471no—
443C2×C8—471no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8C2×C4×D4711yescharacteristic
448C2×C8C2×C4×D4711yescharacteristic
449C2×C8D4×D4711yescharacteristic
450C2×C8D4×D4711yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—471no—
454C4⋊C4—471no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4C2×C4×D4711yescharacteristic
466C4⋊C4C2×C4×D4711yescharacteristic
467C22⋊C4—941no—
468C22⋊C4—941no—
469C42—21no—
470C42—21no—
471C42—471no—
472C42—471no—
473C42—471no—
474C42—941no—
475C42—941no—
476C42—941no—
477C42—941no—
478C42C23×D4711yescharacteristic
479C23—471no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—472no—
484Q8—944no—
485Q8—941no—
486Q8—941no—
487Q8—941no—
488Q8—3761no—
489Q8#1309403012yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—471no—
495C2×C4—471no—
496C2×C4—471no—
497C2×C4—944no—
498C2×C4—941no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—941no—
502C2×C4—941no—
503C2×C4—941no—
504C2×C4—941no—
505C2×C4—941no—
506C2×C4—3761no—
507C2×C4—1881no—
508C2×C4C22×C4×D4711yescharacteristic
509C2×C4C2×D4×D4711yescharacteristic
510C2×C4#41×D4711yescharacteristic
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—942no—
519C8—941no—
520C8—941no—
521C8—941no—
522C8—941no—
523C8—1881no—
524C8—1881no—
525C22—941no—
526C22—941no—
527C22—941no—
528C22C4×D4×D4711yescharacteristic
529C4—21no—
530C4—22no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—941no—
535C4—941no—
536C4—941no—
537C4—942no—
538C4—1881no—
539C4—1881no—
540C4—1881no—
541C4#131×D4711yescharacteristic
542C4C2×#1309403011yescharacteristic
543C4#1568993911yescharacteristic
544C4#1568993911yescharacteristic
545C2—1881no—
546C2#2025207711yescharacteristic
547C2#2025225311yescharacteristic
548C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1579C2
socleC22×C47C2×C4×D4
prime radicalC22×D47C4×D4
cosocleC42×C47C24
hypercenter#1579D47
hypocenterC47#17925
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
4. #20242260C2semidirect
5. #20242258C2semidirect
6. #20242241C2semidirect
7. #20242235C2semidirect
8. #20242208C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625337C2semidirect
15. C47×#1579C2semidirect
279. #1579D47semidirect
341. C47#17925semidirect

Maximal subgroups

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

subgroupindex
#202534252
#202524792
#202524672
#202422602
#202422582
#202422412
#202422352
#202422082
C8×#106253372
#202421652
#202418332
#202418072
#202416842
C47×#15792
#1792547