Finite Group Databasebeta

← #25149959

Subgroups — #25149959

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2C2×#14583268C211yesmaximal, characteristic, complemented
3C2×#14583110C211yesmaximal, characteristic, complemented
4#19139548C211yesmaximal, characteristic
5#19135605C212yesmaximal, complemented
6#19135605C212yesmaximal, complemented
7#19135550C211yesmaximal, characteristic, complemented
8#19134905C212yesmaximal, complemented
9#19134900C212yesmaximal, complemented
10#19134426C211yesmaximal, characteristic, complemented
11C43×#1955C211yesmaximal, characteristic
12C22×Dic172C2212yes—
13#14583589—24no—
14#14583589—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063318—21no—
17C2×#13063317C2211yescharacteristic
18C2×#13063315—21no—
19C2×#13063306—21no—
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2212yes—
23C2×#13063304C2212yes—
24C2×C4×Dic86C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26C2×#13063281—21no—
27C22×C4⋊Dic43C2211yescharacteristic
28#14583268—24no—
29#14583110—24no—
30C2×#13063250C2212yes—
31C2×#13063250C2212yes—
32C2×#13063250C2212yes—
33C2×#13063250C2212yes—
34#14582835—21no—
35#14582835—21no—
36#14582802—21no—
37#14582768—21no—
38C4×C4⋊Dic43C2211yescharacteristic
39#14582662C2212yes—
40#14582662C2212yes—
41#14582662C2212yes—
42C2×C4×D4×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2212yes—
45C2×C22⋊C8×C43C2212yes—
46C2×#97×C43C2211yescharacteristic
47C22×Dic86C2312yes—
48C22×Dic86C2311yescharacteristic
49C23×Dic43—21no—
50C2×Dic172—24no—
51C2×Dic172—42no—
52C2×Dic172—42no—
53#13063325—22no—
54#13063325—22no—
55#13063318—28no—
56#13063317—22no—
57#13063317D414yes—
58#13063315—28no—
59#13063306—28no—
60#13063304—22no—
61#13063304—22no—
62#13063304—22no—
63#13063304—22no—
64#13063304—24no—
65#13063304—24no—
66#13063304—42no—
67#13063304—42no—
68C4×Dic86—22no—
69C4×Dic86D414yes—
70#13063284—22no—
71#13063284—22no—
72#13063281—28no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2312yes—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—22no—
93C2×C22⋊Dic43—22no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97#13063250—24no—
98#13063250—24no—
99#13063250—24no—
100#13063250—24no—
101C43⋊#95—21no—
102C22×D4×C43D411yescharacteristic
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C22×C8×C43C2312yes—
106C22×C8×C43C2312yes—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C42×C43C2311yescharacteristic
113C4⋊C8×C43—22no—
114C22⋊C8×C43—42no—
115C22⋊C8×C43—42no—
116#97×C43—22no—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—41no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—24no—
136C22×Dic43—22no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C2×Dic86—22no—
145C2×Dic86—22no—
146C2×Dic86—21no—
147C2×Dic86—22no—
148C2×Dic86—22no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—22no—
153C2×Dic86C2×D412yes—
154C2×C8×C43—22no—
155C2×C8×C43—22no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C4⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C42×C43C2×D412yes—
164C42×C43C2×D412yes—
165C22⋊Dic43—24no—
166C22⋊Dic43—24no—
167C22⋊Dic43—24no—
168C22⋊Dic43—44no—
169C22⋊Dic43—44no—
170C4⋊Dic43—24no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—22no—
175C4⋊Dic43—42no—
176C4⋊Dic43—42no—
177C4⋊Dic43C2×D412yes—
178C4⋊Dic43C2×D412yes—
179C4⋊Dic43C2×D412yes—
180C4⋊Dic43#4114yes—
181Dic43⋊C4—24no—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—44no—
187Dic43⋊C4—44no—
188C4×Dic43—24no—
189C4×Dic43—24no—
190C4×Dic43—42no—
191Dic172—48no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—21no—
195C23×C43—22no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—22no—
201C23×C43#13712yes—
202C23×C43C22×D411yescharacteristic
203D4×C43—44no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43#12012yes—
218C2×C4×C43#12012yes—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4112yes—
222C2×C4×C43H(5,𝔽2)12yes—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—48no—
229C2×Dic43—42no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240Dic86—22no—
241Dic86—22no—
242Dic86—42no—
243Dic86—42no—
244Dic86—42no—
245Dic86—42no—
246Dic86—42no—
247C8×C43—42no—
248C8×C43—42no—
249#25584—431nomaximal, Sylow
250C22×C43—22no—
251C22×C43—24no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—42no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43C2×#12011yescharacteristic
261C22×C43#54612yes—
262C22×C43C2×#13711yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57812yes—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43#53211yescharacteristic
270C4×C43#53511yescharacteristic
271C4×C43#55012yes—
272Dic43—42no—
273Dic43—42no—
274Dic43—42no—
275Dic43—42no—
276Dic43—44no—
277Dic43—82no—
278C2×#552—431no—
279C2×#491—431no—
280C2×#462—431no—
281#2542—431no—
282#2001—432no—
283#2001—432no—
284#1989—431no—
285#1955D4311yescharacteristic
286#1873—432no—
287#1872—432no—
288#1763—431no—
289C2×C43—42no—
290C2×C43—81no—
291C2×C43#243111yescharacteristic
292C2×C43#300711yescharacteristic
293C2×C43#301111yescharacteristic
294C2×C43#331212yes—
295C2×C43#331512yes—
296C22×Q16—432no—
297#552—864no—
298#552—864no—
299C2×C4⋊Q8—431no—
300C2×#126—861no—
301C2×#125—431no—
302C2×#125—861no—
303C2×#123—861no—
304C2×C22⋊Q8—431no—
305C2×C22⋊Q8—431no—
306C2×C22⋊Q8—432no—
307C2×C22⋊Q8—432no—
308C2×C4×Q8—431no—
309C2×C4×D4C2×D4311yescharacteristic
310C2×#117—431no—
311C2×#117—861no—
312C22×C4⋊C4—431no—
313#491—864no—
314#462—864no—
315C2×C4⋊C8C2×D4311yescharacteristic
316C2×#103—432no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#103—432no—
320C2×C22⋊C8C2×D4312yes—
321C2×C22⋊C8C2×D4312yes—
322C2×#97C2×D4311yescharacteristic
323#399—861no—
324#399—861no—
325#390—861no—
326#384—861no—
327C4×C4⋊C4—431no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2558411yescharacteristic, complemented, Sylow
332C22×Q8—431no—
333C22×Q8—432no—
334C22×D4D17211yescharacteristic
335C23×C4—861no—
336C23×C4C22×D4311yescharacteristic
337C23×C4C22×D4311yescharacteristic
338C2×Q16—864no—
339C2×Q16—1722no—
340C2×Q16—1722no—
341C22×C8C22×D4312yes—
342C22×C8C22×D4312yes—
343C4⋊Q8—862no—
344C4⋊Q8—862no—
345#126—868no—
346#125—434no—
347#125—868no—
348#125—862no—
349#123—868no—
350C22⋊Q8—862no—
351C22⋊Q8—862no—
352C22⋊Q8—862no—
353C22⋊Q8—862no—
354C22⋊Q8—864no—
355C22⋊Q8—864no—
356C22⋊Q8—1722no—
357C22⋊Q8—1722no—
358C4×Q8—434no—
359C4×Q8—862no—
360C4×D4—22no—
361C4×D4—22no—
362#117—868no—
363#117—862no—
364#117—862no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—862no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4D17211yescharacteristic
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4D17211yescharacteristic
388C2×C22⋊C4D17211yescharacteristic
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393C4⋊C8—22no—
394#103—864no—
395#103—864no—
396#103—864no—
397#103—864no—
398C22⋊C8—42no—
399C22⋊C8—42no—
400#97—22no—
401#95—861no—
402C24C2×D17211yescharacteristic
403C24C2×D17211yescharacteristic
404C2×Q8—432no—
405C2×Q8—861no—
406C2×Q8—862no—
407C2×Q8—862no—
408C2×Q8—862no—
409C2×Q8—862no—
410C2×Q8—862no—
411C2×Q8—862no—
412C2×Q8—862no—
413C2×Q8—862no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—41no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—864no—
426C22×C4—862no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—1722no—
433C22×C4—1722no—
434C22×C4C2×D17211yescharacteristic
435C22×C4C2×D17211yescharacteristic
436C22×C4C2×D17211yescharacteristic
437C22×C4C2×D17211yescharacteristic
438C22×C4C23×D4311yescharacteristic
439Q16—1728no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—22no—
447C4⋊C4—432no—
448C4⋊C4—432no—
449C4⋊C4—432no—
450C4⋊C4—434no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—864no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—862no—
461C4⋊C4—1724no—
462C4⋊C4—1724no—
463C4⋊C4—1722no—
464C4⋊C4—1722no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—864no—
468C22⋊C4—864no—
469C22⋊C4—864no—
470C22⋊C4—1724no—
471C22⋊C4—1724no—
472C42—864no—
473C42—864no—
474C42—1722no—
475C42D4×D4312yes—
476C42D4×D4312yes—
477C23—21no—
478C23—21no—
479C23—22no—
480C23—22no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—22no—
485C23—22no—
486C23#1306335812yes—
487C23C22×D17211yescharacteristic
488Q8—862no—
489Q8—862no—
490Q8—1722no—
491Q8—1722no—
492Q8—1722no—
493Q8—1722no—
494Q8—1722no—
495D4—44no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—862no—
510C2×C4—862no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—864no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1728no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1722no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306329512yes—
527C2×C4#1306329512yes—
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4#41×D4312yes—
531C2×C4#1306337012yes—
532C8—42no—
533C8—42no—
534C22—24no—
535C22—22no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22C2×#1306329511yescharacteristic
545C22#1458354412yes—
546C22C2×#1306335811yescharacteristic
547C22#1458369911yescharacteristic
548C22#1458371612yes—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—3442no—
554C4—1722no—
555C4—1722no—
556C4—1722no—
557C4—1724no—
558C4—1722no—
559C4#1458344811yescharacteristic
560C4#1458346211yescharacteristic
561C4#1458356712yes—
562C2—42no—
563C2—81no—
564C2#1913821311yescharacteristic
565C2#1914385711yescharacteristic
566C2#1914389211yescharacteristic
567C2#1914664812yes—
568C2#1914669312yes—
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1955C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#1955D43
hypocenterC43#25584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#14583268C2semidirect
3. C2×#14583110C2semidirect
5. #19135605C2semidirect
6. #19135605C2semidirect
7. #19135550C2semidirect
8. #19134905C2semidirect
9. #19134900C2semidirect
10. #19134426C2semidirect
331. C43#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145832682
C2×#145831102
#191395482
#191356052
#191355502
#191349052
#191349002
#191344262
C43×#19552
#2558443