Finite Group Databasebeta

← #26185539

Subgroups — #26185539

Order 12032.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252352C211yesmaximal, characteristic
2#20252055C211yesmaximal, characteristic
3#20252053C211yesmaximal, characteristic
4#20242178C211yesmaximal, characteristic, complemented
5#20242177C211yesmaximal, characteristic, complemented
6#20242170C211yesmaximal, characteristic, complemented
7#20242167C211yesmaximal, characteristic, complemented
8#20242165C211yesmaximal, characteristic, complemented
9#20242156C211yesmaximal, characteristic, complemented
10#20242154C211yesmaximal, characteristic, complemented
11#20242148C211yesmaximal, characteristic, complemented
12#20242138C211yesmaximal, characteristic, complemented
13#20242137C211yesmaximal, characteristic, complemented
14#20242135C211yesmaximal, characteristic, complemented
15C47×#1573C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689252C411yescharacteristic
18#15689252C411yescharacteristic
19#15689198C411yescharacteristic
20#15689198C411yescharacteristic
21#15689197C411yescharacteristic
22#15689197C411yescharacteristic
23#15689193C411yescharacteristic
24#15689193C411yescharacteristic
25#15689185—21no—
26#15689183—21no—
27#15689183—21no—
28#15689181—21no—
29#15689179C2211yescharacteristic
30#15689179C2211yescharacteristic
31#15689179C2211yescharacteristic
32#15689176C2211yescharacteristic
33#15689175C2211yescharacteristic
34#15689175C2211yescharacteristic
35#15689175C2211yescharacteristic
36#15689174C2211yescharacteristic
37#15689174C2211yescharacteristic
38#15689147C2211yescharacteristic
39#15689145C2211yescharacteristic
40C4⋊C8×D47C2211yescharacteristic
41#15689089—21no—
42#15689088—21no—
43#15689080—21no—
44#15689078—21no—
45C4×#10625329C2211yescharacteristic
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688875C2211yescharacteristic
52#15688875C2211yescharacteristic
53#15688875C2211yescharacteristic
54#15688874C2211yescharacteristic
55#15688874C2211yescharacteristic
56#15688873C2211yescharacteristic
57#15688873C2211yescharacteristic
58#15688873C2211yescharacteristic
59#15688873C2211yescharacteristic
60C47×#432C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C2×#10625350D411yescharacteristic
68C2×#10625329—21no—
69C2×#10625329C2×C411yescharacteristic
70C2×#10625329C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×#10625324C2×C411yescharacteristic
73C2×#10625324C2×C411yescharacteristic
74C2×C8×D47—21no—
75C2×C8×D47C2×C411yescharacteristic
76C2×C8×D47C2×C411yescharacteristic
77C4×Dic94C2×C411yescharacteristic
78C4×Dic94Q811yescharacteristic
79C4×D188C2×C411yescharacteristic
80C4×D188Q811yescharacteristic
81C4×C22⋊D47C2×C411yescharacteristic
82C4×C22⋊D47C2×C411yescharacteristic
83C4×C22⋊D47Q811yescharacteristic
84C4×C22⋊D47Q811yescharacteristic
85#13093983D411yescharacteristic
86#13093981D411yescharacteristic
87#13093981D411yescharacteristic
88C42×D47C2311yescharacteristic
89C42×D47C2311yescharacteristic
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)C2311yescharacteristic
92C4⋊(C47⋊C8)C2311yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94C4⋊(C47⋊C8)C2311yescharacteristic
95Dic47⋊C8—21no—
96Dic47⋊C8—21no—
97Dic47⋊C8C2×C411yescharacteristic
98Dic47⋊C8C2×C411yescharacteristic
99Dic47⋊C8C2×C411yescharacteristic
100Dic47⋊C8C2×C411yescharacteristic
101C22⋊(C47⋊C8)—21no—
102(C2×D47)⋊C8—21no—
103(C2×D47)⋊C8—21no—
104(C2×D47)⋊C8—21no—
105(C2×D47)⋊C8—21no—
106(C2×D47)⋊C8—21no—
107(C2×D47)⋊C8—21no—
108(C2×D47)⋊C8C2×C411yescharacteristic
109(C2×D47)⋊C8C2×C411yescharacteristic
110(C2×D47)⋊C8C2×C411yescharacteristic
111(C2×D47)⋊C8C2×C411yescharacteristic
112#13093935C2×C411yescharacteristic
113#13093935C2×C411yescharacteristic
114#13093934—21no—
115#13093934—21no—
116#13093934—21no—
117#13093934C2×C411yescharacteristic
118#13093934C2×C411yescharacteristic
119C4×C47⋊C8—21no—
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C8×Dic47—21no—
123C8×Dic47—21no—
124C8×Dic47—21no—
125C8×Dic47C2×C411yescharacteristic
126C8×Dic47C2×C411yescharacteristic
127C22×C8×C47—21no—
128C2×C42×C47C2311yescharacteristic
129C4⋊C8×C47—21no—
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47C2×C411yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C22⋊C8×C47—21no—
137C22⋊C8×C47C2×C411yescharacteristic
138C22⋊C8×C47C2×C411yescharacteristic
139#97×C47—21no—
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×Q811yescharacteristic
145C2×C22⋊D47C4⋊C411yescharacteristic
146C2×C22⋊D47C4⋊C411yescharacteristic
147#10625350—41no—
148#10625350—41no—
149C2×D188C4⋊C411yescharacteristic
150C2×C4×D47C22×C411yescharacteristic
151C2×C4×D47C22×C411yescharacteristic
152C2×C4×D47C2×D411yescharacteristic
153C2×C4×D47C2×D411yescharacteristic
154C2×C4×D47C2×Q811yescharacteristic
155C2×C4×D47C2×Q811yescharacteristic
156C2×Dic94C4⋊C411yescharacteristic
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—42no—
162C2×C8×C47C22×C411yescharacteristic
163C2×C8×C47C22×C411yescharacteristic
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C42×C47C22×C411yescharacteristic
167C42×C47C2×D411yescharacteristic
168C42×C47C2×Q811yescharacteristic
169C42×C47C2411yescharacteristic
170C22⋊Dic47C4⋊C411yescharacteristic
171C22⋊Dic47C4⋊C411yescharacteristic
172(C2×D47)⋊C4C4⋊C411yescharacteristic
173(C2×D47)⋊C4C4⋊C411yescharacteristic
174(C2×D47)⋊C4C4⋊C411yescharacteristic
175(C2×D47)⋊C4C4⋊C411yescharacteristic
176C4⋊Dic47C4⋊C411yescharacteristic
177C4⋊Dic47C4⋊C411yescharacteristic
178Dic47⋊C4C4⋊C411yescharacteristic
179Dic47⋊C4C4⋊C411yescharacteristic
180Dic47⋊C4C4⋊C411yescharacteristic
181Dic47⋊C4C4⋊C411yescharacteristic
182C4×Dic47C22×C411yescharacteristic
183C4×Dic47C22×C411yescharacteristic
184C4×Dic47C2×D411yescharacteristic
185C4×Dic47C2×D411yescharacteristic
186C4×Dic47C2×Q811yescharacteristic
187C4×Dic47C2×Q811yescharacteristic
188#10625329—22no—
189#10625329—41no—
190#10625329—42no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8C22×C411yescharacteristic
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C22×C411yescharacteristic
199#10625324—22no—
200#10625324—41no—
201#10625324—42no—
202C8×D47—22no—
203C8×D47—41no—
204C8×D47—42no—
205C23×C47C2×C4⋊C411yescharacteristic
206C22×D47C2×C4⋊C411yescharacteristic
207C22×D47C2×C4⋊C411yescharacteristic
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—41no—
213C2×C4×C47C2×C4⋊C411yescharacteristic
214C2×C4×C47C2×C4⋊C411yescharacteristic
215C2×C4×C47C2×C4⋊C411yescharacteristic
216C2×C4×C47C23×C411yescharacteristic
217C2×C4×C47C22×D411yescharacteristic
218C2×C4×C47C22×Q811yescharacteristic
219C22⋊D47—41no—
220C22⋊D47—41no—
221C2×Dic47C2×C4⋊C411yescharacteristic
222C2×Dic47C2×C4⋊C411yescharacteristic
223C2×Dic47C2×C4⋊C411yescharacteristic
224C2×Dic47C2×C4⋊C411yescharacteristic
225C2×Dic47C2×C4⋊C411yescharacteristic
226C2×Dic47C2×C4⋊C411yescharacteristic
227D188—41no—
228C4×D47—21no—
229C4×D47—21no—
230C4×D47—21no—
231C4×D47—21no—
232C4×D47—21no—
233C4×D47—21no—
234C4×D47—21no—
235C4×D47—21no—
236C4×D47—41no—
237C4×D47—41no—
238Dic94—41no—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—41no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8#13112yes—
255#17831—471nomaximal, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—21no—
259C22×C47C22×C4⋊C411yescharacteristic
260C2×D47—21no—
261C2×D47—21no—
262C2×D47—21no—
263C2×D47—21no—
264C2×D47—21no—
265C2×D47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—21no—
269C4×C47—21no—
270C4×C47C2×#13111yescharacteristic
271C4×C47#56811yescharacteristic
272C4×C47#57511yescharacteristic
273C4×C47#57511yescharacteristic
274Dic47—21no—
275Dic47—21no—
276Dic47—21no—
277Dic47—21no—
278Dic47—21no—
279Dic47—21no—
280#2965—471no—
281#2925—471no—
282#2925—471no—
283#1574—471no—
284#1574—471no—
285#1573—471no—
286#1573D4711yescharacteristic, complemented
287#1572—471no—
288#1572—471no—
289#1569—471no—
290#1569—471no—
291#1568—471no—
292#1565—471no—
293#1565—471no—
294#1564—471no—
295C2×C47—41no—
296C2×C47#290611yescharacteristic
297C2×C47#291111yescharacteristic
298C2×C47#291611yescharacteristic
299D47—41no—
300D47—41no—
301C4×#41—471no—
302#446—471no—
303#446—471no—
304#436—471no—
305#436—471no—
306#435—471no—
307#435—471no—
308#435—471no—
309#435—471no—
310#433—941no—
311#433—941no—
312#433—941no—
313#433—941no—
314#432—471no—
315#432—471no—
316#432—471no—
317#432C2×D4711yescharacteristic
318#431—471no—
319#431—471no—
320#431—471no—
321#431—471no—
322#431—471no—
323#431—471no—
324#431C2×D4711yescharacteristic
325#423—471no—
326#423—471no—
327C2×C4⋊C8—471no—
328C2×C4⋊C8C2×D4711yescharacteristic
329#408—941no—
330#408—941no—
331#405—941no—
332#405—941no—
333C4×M16—471no—
334C4×M16—471no—
335C2×C4×C8—471no—
336#335—471no—
337#335—471no—
338#335—471no—
339#335—471no—
340#335—471no—
341#335—471no—
342#335C2×D4711yescharacteristic
343#335C2×D4711yescharacteristic
344#334—471no—
345#334—471no—
346#334—471no—
347#334—471no—
348#334—471no—
349#334—471no—
350#334C2×D4711yescharacteristic
351#334C2×D4711yescharacteristic
352C47#1783111yescharacteristic, complemented, Sylow
353C2×#41—471no—
354C2×M16—471no—
355C2×M16—471no—
356C2×M16—471no—
357C2×M16—471no—
358C2×M16—941no—
359C2×M16—941no—
360C22×C8—21no—
361C22×C8—471no—
362C22×C8—471no—
363C22×C8—941no—
364C4×Q8—471no—
365C4×Q8—471no—
366C4×D4—471no—
367C4×D4—471no—
368C4×D4—471no—
369C4×D4—471no—
370C4×D4—471no—
371C4×D4—471no—
372#117—471no—
373#117—471no—
374#117—471no—
375C2×C42—471no—
376C2×C42—471no—
377C2×C42C22×D4711yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—471no—
380C4⋊C8—471no—
381C4⋊C8—471no—
382C4⋊C8—471no—
383C4⋊C8—471no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8C4×D4711yescharacteristic
391C4⋊C8C4×D4711yescharacteristic
392C4⋊C8C22×D4711yescharacteristic
393C4⋊C8C22×D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—471no—
398C22⋊C8—471no—
399C22⋊C8—471no—
400C22⋊C8—471no—
401C22⋊C8—941no—
402C22⋊C8—941no—
403C22⋊C8—941no—
404C22⋊C8—941no—
405C22⋊C8—941no—
406C22⋊C8—941no—
407C22⋊C8—941no—
408C22⋊C8C4×D4711yescharacteristic
409C22⋊C8C4×D4711yescharacteristic
410#97—21no—
411#97—471no—
412#97—471no—
413#97—471no—
414#97—471no—
415#97—941no—
416#97—941no—
417#97—941no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8—941no—
426C4×C8C22×D4711yescharacteristic
427C4×C8C22×D4711yescharacteristic
428#41—1881no—
429#41—1881no—
430C2×Q8—471no—
431C2×D4—471no—
432C2×D4—471no—
433C2×D4—471no—
434C22×C4—471no—
435C22×C4—471no—
436C22×C4—471no—
437C22×C4—471no—
438C22×C4—471no—
439C22×C4—471no—
440C22×C4C2×C4×D4711yescharacteristic
441C22×C4D4×D4711yescharacteristic
442C22×C4Q8×D4711yescharacteristic
443M16—942no—
444M16—942no—
445M16—1881no—
446M16—1882no—
447M16—1881no—
448M16—1882no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—942no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—1881no—
464C2×C8—1882no—
465C2×C8C2×C4×D4711yescharacteristic
466C2×C8C2×C4×D4711yescharacteristic
467C2×C8C2×C4×D4711yescharacteristic
468C2×C8C2×C4×D4711yescharacteristic
469C4⋊C4—471no—
470C4⋊C4—471no—
471C4⋊C4—471no—
472C4⋊C4—471no—
473C4⋊C4—471no—
474C4⋊C4—471no—
475C22⋊C4—471no—
476C22⋊C4—471no—
477C22⋊C4—471no—
478C22⋊C4—471no—
479C22⋊C4—471no—
480C22⋊C4—471no—
481C42—471no—
482C42—471no—
483C42—471no—
484C42—471no—
485C42—471no—
486C42—471no—
487C42C2×C4×D4711yescharacteristic
488C42D4×D4711yescharacteristic
489C42Q8×D4711yescharacteristic
490C42C23×D4711yescharacteristic
491C23—471no—
492C23—471no—
493C23C4⋊C4×D4711yescharacteristic
494Q8—1881no—
495D4—1881no—
496D4—1881no—
497D4—1881no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—471no—
504C2×C4—471no—
505C2×C4—471no—
506C2×C4—471no—
507C2×C4—471no—
508C2×C4—471no—
509C2×C4—941no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—1881no—
518C2×C4—1881no—
519C2×C4C4⋊C4×D4711yescharacteristic
520C2×C4C4⋊C4×D4711yescharacteristic
521C2×C4C4⋊C4×D4711yescharacteristic
522C2×C4C22×C4×D4711yescharacteristic
523C2×C4C2×D4×D4711yescharacteristic
524C2×C4C2×Q8×D4711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—472no—
534C8—941no—
535C8—941no—
536C8—941no—
537C8—1881no—
538C8—1881no—
539C8—1881no—
540C8—1881no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—941no—
545C22—941no—
546C22—941no—
547C22—941no—
548C22—941no—
549C22—941no—
550C22C2×C4⋊C4×D4711yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—941no—
556C4—941no—
557C4—941no—
558C4—941no—
559C4—941no—
560C4—941no—
561C4#131×D4711yescharacteristic
562C4#1568988811yescharacteristic
563C4#1568991911yescharacteristic
564C4#1568992211yescharacteristic
565C2—41no—
566C2—1881no—
567C2—1881no—
568C2#2025195511yescharacteristic
569C2#2025197511yescharacteristic
570C2#2025199611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1573C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#10625350D4
cosocleC42×C47C24
hypercenter#1573D47
hypocenterC47#17831
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
4. #20242178C2semidirect
5. #20242177C2semidirect
6. #20242170C2semidirect
7. #20242167C2semidirect
8. #20242165C2semidirect
9. #20242156C2semidirect
10. #20242154C2semidirect
11. #20242148C2semidirect
12. #20242138C2semidirect
13. #20242137C2semidirect
14. #20242135C2semidirect
15. C47×#1573C2semidirect
286. #1573D47semidirect
352. C47#17831semidirect

Maximal subgroups

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

subgroupindex
#202523522
#202520552
#202520532
#202421782
#202421772
#202421702
#202421672
#202421652
#202421562
#202421542
#202421482
#202421382
#202421372
#202421352
C47×#15732
#1783147