Finite Group Databasebeta

← #24989348

Subgroups — #24989348

Order 11008.

742 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic43C211yesmaximal, characteristic
2#19134573C211yesmaximal, characteristic, complemented
3C2×#14582633C211yesmaximal, characteristic
4Dic43⋊#95C211yesmaximal, characteristic, complemented
5#19132475C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C2×D4×Dic43C411yescharacteristic, complemented
10C22×Dic43⋊C4—21no—
11C22×C4×Dic43C2211yescharacteristic
12C2×Dic43⋊C8—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582802C411yescharacteristic, complemented
15#14582798C411yescharacteristic, complemented
16#14582792—21no—
17#14582779—21no—
18#14582759C2211yescharacteristic
19C4⋊C4×Dic43C411yescharacteristic, complemented
20C22⋊C4×Dic43—21no—
21C2×C43⋊#95—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582653—21no—
24#14582633—22no—
25C2×#121×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×#95×C43C2211yescharacteristic
28C43×#327—22no—
29C23×Dic43—21no—
30C23×Dic43—21no—
31C23×Dic43D411yescharacteristic
32C23×Dic43D411yescharacteristic
33C22×C43⋊C8—21no—
34D4×Dic43—42no—
35D4×Dic43—42no—
36D4×Dic43—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×Dic43⋊C4—24no—
41C2×Dic43⋊C4—42no—
42C2×Dic43⋊C4—42no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—42no—
49C2×C4×Dic43C2×C411yescharacteristic
50C2×C4×Dic43C2×C411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53Dic43⋊C8—42no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—42no—
62C22×D4×C43—21no—
63C22×D4×C43C2×C411yescharacteristic
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69#121×C43D412yes—
70#121×C43Q812yes—
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75#95×C43—21no—
76#95×C43—21no—
77C24×C43—21no—
78C24×C43C2×D411yescharacteristic
79C2×D4×C43—21no—
80C2×D4×C43—22no—
81C2×D4×C43—22no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43C4⋊C412yescomplemented
89C22×C4×C43—22no—
90C22×C4×C43—21no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43C22×C411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×Q811yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×Dic43—22no—
106C22×Dic43—22no—
107C22×Dic43—22no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43—41no—
117C22×Dic43—42no—
118C22×Dic43—42no—
119C22×Dic43—42no—
120C22×Dic43—41no—
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43C22⋊C411yescharacteristic
124C22×Dic43C22⋊C411yescharacteristic
125C22×Dic43C22⋊C411yescharacteristic
126C22×Dic43C22⋊C411yescharacteristic
127C22×Dic43D812yes—
128C22×Dic43SD1612yes—
129C2×C8×C43—41no—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43C4⋊C412yescomplemented
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊Dic43—42no—
137C22⋊Dic43—42no—
138C22⋊Dic43—42no—
139C22⋊Dic43—41no—
140C22⋊Dic43—41no—
141C4⋊Dic43—42no—
142C4⋊Dic43—41no—
143C4⋊Dic43—41no—
144Dic43⋊C4—48no—
145C4×Dic43—22no—
146C4×Dic43—22no—
147C4×Dic43—41no—
148C4×Dic43—41no—
149C4×Dic43—42no—
150C2×C43⋊C8—41no—
151C2×C43⋊C8—41no—
152C2×C43⋊C8—41no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—22no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43C2×C22⋊C411yescharacteristic
165C23×C43#12111yescharacteristic
166C23×C43C22⋊Q811yescharacteristic
167C23×C43C2×D811yescharacteristic
168C23×C43C2×SD1611yescharacteristic
169C23×C43AGL(1,ℤ/8)11yescharacteristic
170C23×C43#13711yescharacteristic
171D4×C43—42no—
172D4×C43—42no—
173D4×C43—42no—
174D4×C43—42no—
175D4×C43—42no—
176D4×C43—42no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—22no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—42no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—81no—
192C2×C4×C43—81no—
193C2×C4×C43—81no—
194C2×C4×C43—81no—
195C2×C4×C43C2×C4⋊C411yescharacteristic
196C2×C4×C43#11711yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43C22⋊Q811yescharacteristic
199C2×Dic43—24no—
200C2×Dic43—24no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—21no—
209C2×Dic43—42no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—84no—
221C2×Dic43—81no—
222C2×Dic43—81no—
223C2×Dic43—81no—
224C2×Dic43—81no—
225C2×Dic43#9912yes—
226C2×Dic43#10212yes—
227C2×Dic43#10212yes—
228C2×Dic43#10412yes—
229C8×C43—81no—
230C43⋊C8—81no—
231#8577—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—42no—
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43#38011yescharacteristic
252C22×C43C2×#9911yescharacteristic
253C22×C43#41011yescharacteristic
254C22×C43C2×#10211yescharacteristic
255C22×C43#41711yescharacteristic
256C22×C43C2×#10411yescharacteristic
257C22×C43#42111yescharacteristic
258C22×C43#45911yescharacteristic
259C22×C43#46111yescharacteristic
260C22×C43#47411yescharacteristic
261C22×C43#47611yescharacteristic
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—42no—
267C4×C43—82no—
268Dic43—22no—
269Dic43—22no—
270Dic43—22no—
271Dic43—22no—
272Dic43—82no—
273Dic43—81no—
274Dic43—81no—
275C4×#121—431no—
276#1797—431no—
277C2×#327—431no—
278C2×#327D4311yescharacteristic
279C4⋊#95—431no—
280#1294—431no—
281#1294—431no—
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—21no—
285C2×C43—21no—
286C2×C43—82no—
287C2×C43#150211yescharacteristic
288C2×C43#150411yescharacteristic
289C2×C43#151211yescharacteristic
290C2×C43#151911yescharacteristic
291C2×C43#179911yescharacteristic
292C2×C43#180211yescharacteristic
293C2×C43#180611yescharacteristic
294C2×#121C2×D4311yescharacteristic
295C2×C4×D4—431no—
296C2×C4×D4—861no—
297C22×C4⋊C4—861no—
298C22×C42—431no—
299C2×C4⋊C8—861no—
300C2×C22⋊C8—431no—
301C2×C22⋊C8C2×D4311yescharacteristic
302#390—431no—
303#389—431no—
304#388—861no—
305#386—861no—
306#380—431no—
307C4×C4⋊C4—431no—
308C4×C22⋊C4—861no—
309C2×#95—431no—
310C2×#95—861no—
311C2×#95C2×D4311yescharacteristic
312#336—861no—
313#327—22no—
314#327—862no—
315C43#857711yescharacteristic, complemented, Sylow
316C22×D4—21no—
317C22×D4C4×D4311yescharacteristic
318C23×C4—21no—
319C23×C4—431no—
320C23×C4—431no—
321C23×C4—861no—
322C23×C4—861no—
323C23×C4C22×D4311yescharacteristic
324C22×C8—21no—
325C22×C8—861no—
326#121—21no—
327#121—21no—
328#121Dic8612yes—
329#121C22⋊D4312yes—
330C4×D4—1722no—
331C4×D4—1722no—
332C4×D4—1722no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—864no—
337C2×C4⋊C4—1722no—
338C2×C4⋊C4—1722no—
339C2×C4⋊C4C4×D4311yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—861no—
342C2×C22⋊C4—861no—
343C2×C22⋊C4—861no—
344C2×C22⋊C4—861no—
345C2×C42—431no—
346C2×C42—431no—
347C2×C42—431no—
348C2×C42—431no—
349C2×C42—861no—
350C2×C42—1722no—
351C4⋊C8—1722no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—861no—
355C22⋊C8—861no—
356#95—21no—
357#95—21no—
358#95—861no—
359#95—861no—
360#95—861no—
361#95—861no—
362#95—861no—
363#95—1722no—
364C24—21no—
365C24D4×D4311yescharacteristic
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4Dic43⋊C412yescomplemented
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—431no—
387C22×C4—431no—
388C22×C4—431no—
389C22×C4—431no—
390C22×C4—432no—
391C22×C4—432no—
392C22×C4—862no—
393C22×C4—862no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—862no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—1722no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1722no—
403C22×C4—1722no—
404C22×C4—1721no—
405C22×C4—1721no—
406C22×C4—1721no—
407C22×C4—1721no—
408C22×C4—1721no—
409C22×C4—1721no—
410C22×C4C2×Dic8611yescharacteristic
411C22×C4C2×C4×D4311yescharacteristic
412C22×C4D4×D4311yescharacteristic
413C22×C4#1062190011yescharacteristic
414C22×C4#1062190011yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—1721no—
420C2×C8—1721no—
421C2×C8—1721no—
422C4⋊C4—21no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4—1722no—
426C4⋊C4—1728no—
427C4⋊C4Dic43⋊C412yescomplemented
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—1722no—
431C22⋊C4—1722no—
432C22⋊C4—1722no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C42—862no—
436C42—862no—
437C42—1721no—
438C42—1721no—
439C42—1722no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C22⋊C4×D4311yescharacteristic
452C23#1306329711yescharacteristic
453C23#1306330211yescharacteristic
454C23D8×D4311yescharacteristic
455C23SD16×D4311yescharacteristic
456C23#1306334911yescharacteristic
457C23#1306335411yescharacteristic
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—432no—
483C2×C4—432no—
484C2×C4—432no—
485C2×C4—432no—
486C2×C4—864no—
487C2×C4—864no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—3444no—
497C2×C4—3441no—
498C2×C4—3441no—
499C2×C4—3441no—
500C2×C4—3441no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4C2×Dic43⋊C411yescharacteristic
513C2×C4#1306328111yescharacteristic
514C2×C4#1306329711yescharacteristic
515C2×C4#1306330211yescharacteristic
516C8—81no—
517C8—3441no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#1458275711yescharacteristic
538C22#99×D4311yescharacteristic
539C22#1458287111yescharacteristic
540C22#102×D4311yescharacteristic
541C22#1458289711yescharacteristic
542C22#104×D4311yescharacteristic
543C22#1458291411yescharacteristic
544C22#1458309211yescharacteristic
545C22#1458310211yescharacteristic
546C22#1458317711yescharacteristic
547C22#1458318711yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—82no—
554C4—862no—
555C4—862no—
556C4—862no—
557C4—862no—
558C4—3442no—
559C4—3441no—
560C4—3441no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—82no—
566C2#1913308811yescharacteristic
567C2#1913309611yescharacteristic
568C2#1913313011yescharacteristic
569C2#1913316111yescharacteristic
570C2#1913458111yescharacteristic
571C2#1913459311yescharacteristic
572C2#1913461311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#8577
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #19134573C2semidirect
4. Dic43⋊#95C2semidirect
5. #19132475C2semidirect
6. #19132474C2semidirect
9. C2×D4×Dic43C4semidirect
14. #14582802C4semidirect
15. #14582798C4semidirect
19. C4⋊C4×Dic43C4semidirect
88. C2×D4×C43C4⋊C4semidirect
133. C4⋊C4×C43C4⋊C4semidirect
315. C43#8577semidirect
375. C2×D4Dic43⋊C4semidirect
427. C4⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
#121×Dic432
#191345732
C2×#145826332
Dic43⋊#952
#191324752
#191324742
C2×C43×#3272
#857743