Finite Group Databasebeta

← #25081938

Subgroups — #25081938

Order 11008.

644 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#19145719C211yesmaximal, characteristic
2#477×D43C211yesmaximal, characteristic, complemented
3#19144062C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic, complemented
5#19134010C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19134008C211yesmaximal, characteristic, complemented
8#19133980C211yesmaximal, characteristic, complemented
9#19133979C211yesmaximal, characteristic, complemented
10#19133978C211yesmaximal, characteristic, complemented
11#19133977C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic
15C43×#1678C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17#14583447C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583216—21no—
24#14583216—21no—
25#14583195C2211yescharacteristic
26#14583194C2211yescharacteristic
27#14583193—21no—
28#14583192—21no—
29#14583191C2211yescharacteristic
30#14583187—21no—
31#14583187—21no—
32#14583120—21no—
33#14583119—21no—
34#14583110C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583096C2211yescharacteristic
37Q8×C43⋊C8C2211yescharacteristic
38C8×Dic86—21no—
39C8×Dic86C2211yescharacteristic
40#14583023—21no—
41#14583023C2211yescharacteristic
42#14582951—21no—
43#14582951C2211yescharacteristic
44#14582950—21no—
45#14582950C2211yescharacteristic
46#107×D43—21no—
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582897—21no—
50#103×D43—21no—
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43D411yescharacteristic
70#13063354—44no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063323—21no—
81#13063312—21no—
82#13063296—21no—
83#13063296—21no—
84Q8×Dic43D411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290D411yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43D411yescharacteristic
95C42×D43—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114#13063250—21no—
115#13063250—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×C22⋊D43—41no—
151C22×Dic43—41no—
152Q8×D43—22no—
153Q8×D43—82no—
154Q8×D43SD1614yes—
155#10621900—42no—
156#10621900—42no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—41no—
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×Dic86C2×D411yescharacteristic
168SD16×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182#10621885—42no—
183#10621883—42no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207#10621872—42no—
208C8×D43—42no—
209C23×C43—41no—
210C22×D43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—81no—
213Q8×C43C2×SD1612yes—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—82no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—82no—
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C4×D43—24no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—41no—
238C4×D43—81no—
239C4×D43—82no—
240C4×D43C2×SD1612yes—
241C4×D43#13512yes—
242Dic86—21no—
243Dic86—24no—
244Dic86—41no—
245Dic86—41no—
246Dic86—82no—
247Dic86—81no—
248Dic86C2×SD1612yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19403—431nomaximal, Sylow
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×#12111yescharacteristic
264C2×D43—21no—
265C2×D43—21no—
266C2×D43#46512yes—
267C4×C43—22no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43C22×SD1611yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43#57811yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—21no—
276Dic43—22no—
277Dic43—21no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281Dic43#46512yes—
282#3227—431no—
283C2×#477—431no—
284#3037—431no—
285#2982—431no—
286#1678—431no—
287#1678—431no—
288#1678—431no—
289#1678D4311yescharacteristic, complemented
290#1672—431no—
291#1672—431no—
292#1672—431no—
293#1672—431no—
294#1570—431no—
295#1548—431no—
296#1540—431no—
297C2×C43—161no—
298C2×C43#304411yescharacteristic
299C2×C43C2×#46511yescharacteristic
300C2×C43#306811yescharacteristic
301D43—22no—
302C2×#137—861no—
303#532—431no—
304C2×C4⋊Q8—431no—
305C2×C4×Q8—431no—
306#498—431no—
307#498—431no—
308#486—431no—
309#486C2×D4311yescharacteristic
310#481—861no—
311#481—861no—
312#477—431no—
313#477—431no—
314#477—431no—
315#477—861no—
316#477—861no—
317#477C2×D4311yescharacteristic
318#476—861no—
319#476—861no—
320#464—861no—
321#464—861no—
322#462—431no—
323#462—431no—
324#460—431no—
325#460C2×D4311yescharacteristic
326C8×Q8—431no—
327C8×Q8—431no—
328C8×Q8—431no—
329C8×Q8—861no—
330C8×Q8—861no—
331C8×Q8C2×D4311yescharacteristic
332#431—431no—
333#431—431no—
334#431—861no—
335#431—861no—
336C2×#107—861no—
337#423—431no—
338C2×C4⋊C8—431no—
339#417—861no—
340C2×#103—861no—
341#334—431no—
342#334—431no—
343#334—431no—
344#334C2×D4311yescharacteristic
345#333—431no—
346#333—431no—
347#333—431no—
348#333C2×D4311yescharacteristic
349#332—431no—
350#332—431no—
351#331—431no—
352#331C2×D4311yescharacteristic
353C43#1940311yescharacteristic, complemented, Sylow
354C2×#41—861no—
355C22×Q8—431no—
356C22×Q8—861no—
357#137—1724no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×SD16—21no—
361C2×SD16—861no—
362C2×M16—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8C22×D4311yescharacteristic
370#127C22×D4311yescharacteristic
371#124—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8C22×D4311yescharacteristic
380C4×D4—861no—
381C4×D4—861no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C42—431no—
387C2×C42—861no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—431no—
423C22⋊C8—431no—
424C22⋊C8—861no—
425C4×C8—21no—
426C4×C8—431no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—1722no—
433#41—1722no—
434C2×Q8—21no—
435C2×Q8—434no—
436C2×Q8—431no—
437C2×Q8—861no—
438C2×Q8—862no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3442no—
442C2×Q8—1721no—
443C2×Q8D4×D4311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—1721no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—1721no—
454C22×C4—1721no—
455Q16—1722no—
456Q16—1722no—
457SD16—42no—
458SD16—1722no—
459M16—1722no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8D4×D4311yescharacteristic
470C2×C8D4×D4311yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4D4×D4311yescharacteristic
486C22⋊C4—1721no—
487C22⋊C4—1721no—
488C42—21no—
489C42—431no—
490C42—431no—
491C42—431no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42C23×D4311yescharacteristic
496C23—41no—
497C23—431no—
498Q8—21no—
499Q8—81no—
500Q8—432no—
501Q8—864no—
502Q8—861no—
503Q8—3441no—
504Q8—3442no—
505Q8—1721no—
506Q8—1721no—
507Q8SD16×D4312yes—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—81no—
513D4—3442no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—431no—
518C2×C4—432no—
519C2×C4—432no—
520C2×C4—431no—
521C2×C4—431no—
522C2×C4—864no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3441no—
528C2×C4—3442no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4#41×D4311yescharacteristic
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—432no—
550C22—861no—
551C22—861no—
552C22#121×D4311yescharacteristic
553C4—21no—
554C4—22no—
555C4—41no—
556C4—81no—
557C4—432no—
558C4—861no—
559C4—861no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4C2×SD16×D4311yescharacteristic
565C4#135×D4311yescharacteristic
566C4#1458371311yescharacteristic
567C4#1458371511yescharacteristic
568C2—161no—
569C2—862no—
570C2#1914412311yescharacteristic
571C2#465×D4311yescharacteristic
572C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1678C2
socleC22×C43C2×#121
prime radical#14583447C22
hypercenter#1678D43
hypocenterC43#19403
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1678

Complements

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

NH ≅ G/Ntype
2. #477×D43C2semidirect
4. #19143674C2semidirect
5. #19134010C2semidirect
6. #19134009C2semidirect
7. #19134008C2semidirect
8. #19133980C2semidirect
9. #19133979C2semidirect
10. #19133978C2semidirect
11. #19133977C2semidirect
12. #19133364C2semidirect
13. #19133274C2semidirect
15. C43×#1678C2semidirect
289. #1678D43semidirect
353. C43#19403semidirect

Maximal subgroups

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

subgroupindex
#191457192
#477×D432
#191440622
#191436742
#191340102
#191340092
#191340082
#191339802
#191339792
#191339782
#191339772
#191333642
#191332742
#191332412
C43×#16782
#1940343