Finite Group Databasebeta

← #25081935

Subgroups — #25081935

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#19145724C211yesmaximal, characteristic
2#477×D43C211yesmaximal, characteristic, complemented
3#19144068C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic, complemented
5#19134014C211yesmaximal, characteristic, complemented
6#19134013C211yesmaximal, characteristic, complemented
7#19134012C211yesmaximal, characteristic, complemented
8#19134011C211yesmaximal, characteristic, complemented
9#19133976C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133974C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133243C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16C2×#13063357—21no—
17#14583450C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583219—21no—
24#14583219—21no—
25#14583195C2211yescharacteristic
26#14583194C2211yescharacteristic
27#14583193—21no—
28#14583192—21no—
29#14583191C2211yescharacteristic
30#14583188—21no—
31#14583188—21no—
32#14583124—21no—
33#14583123—21no—
34#14583106C2211yescharacteristic
35#14583100C2211yescharacteristic
36#14583099C2211yescharacteristic
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#14582899—21no—
50#103×D43—21no—
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902—21no—
68C2×Q8×D43—21no—
69C2×Q8×D43D411yescharacteristic
70#13063357—44no—
71C2×#10621885—21no—
72C2×#10621873—21no—
73C2×#10621884—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063323—21no—
80#13063322C2311yescharacteristic
81#13063314—21no—
82#13063300—21no—
83#13063300—21no—
84Q8×Dic43D411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290D411yescharacteristic
89#13063287—21no—
90#13063287—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#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112#13063250—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—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×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148#10621902—42no—
149#10621902—42no—
150Q8×D43—22no—
151Q8×D43—82no—
152Q8×D43SD1614yes—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—41no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43#4111yescharacteristic
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×Dic86C2×D411yescharacteristic
168Q16×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×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C42×C43—21no—
181C42×C43C2411yescharacteristic
182#10621885—42no—
183#10621884—42no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
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
206#10621873—42no—
207#10621872—42no—
208C8×D43—42no—
209C22×D43—41no—
210C22×D43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43C2×SD1612yes—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—41no—
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229D172—41no—
230D172—41no—
231D172—41no—
232D172—41no—
233D172—81no—
234D172—82no—
235C4×D43—24no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—41no—
239C4×D43—81no—
240C4×D43—82no—
241C4×D43—82no—
242C4×D43C2×SD1612yes—
243C4×D43#13512yes—
244Dic86—21no—
245Dic86—24no—
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×C43C2×#12111yescharacteristic
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43#46512yes—
267C4×C43—22no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43C22×SD1611yescharacteristic
273C4×C43C2×#13511yescharacteristic
274C4×C43#57811yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—21no—
277Dic43—22no—
278Dic43—21no—
279Dic43—41no—
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#1678—431no—
290#1672—431no—
291#1672—431no—
292#1672—431no—
293#1672D4311yescharacteristic, complemented
294#1570—431no—
295#1548—431no—
296#1540—431no—
297C2×C43#304411yescharacteristic
298C2×C43C2×#46511yescharacteristic
299C2×C43#306811yescharacteristic
300D43—22no—
301D43—161no—
302C2×#137—861no—
303#532—431no—
304C2×C4⋊Q8—431no—
305C2×C4×Q8—431no—
306#498—431no—
307#498C2×D4311yescharacteristic
308#486—431no—
309#486—431no—
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#462C2×D4311yescharacteristic
324#460—431no—
325#460—431no—
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#332C2×D4311yescharacteristic
351#331—431no—
352#331—431no—
353C43#1940311yescharacteristic, complemented, Sylow
354C2×#41—861no—
355C22×Q8—431no—
356C22×Q8—861no—
357#137—1724no—
358C2×Q16—21no—
359C2×Q16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×M16—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—861no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370#127—431no—
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—21no—
393#106—21no—
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—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#102—861no—
417#102—861no—
418#102—861no—
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—21no—
436C2×Q8—434no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×Q8—862no—
440C2×Q8—861no—
441C2×Q8—3442no—
442C2×Q8—1721no—
443C2×Q8D4×D4311yescharacteristic
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
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—42no—
456Q16—1722no—
457SD16—1722no—
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—21no—
475C4⋊C4—21no—
476C4⋊C4—431no—
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—431no—
497C23—1721no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—432no—
503Q8—864no—
504Q8—861no—
505Q8—3441no—
506Q8—3442no—
507Q8SD16×D4312yes—
508D4—3441no—
509D4—3442no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—431no—
519C2×C4—432no—
520C2×C4—432no—
521C2×C4—431no—
522C2×C4—431no—
523C2×C4—864no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3441no—
529C2×C4—3442no—
530C2×C4—3442no—
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—432no—
547C22—861no—
548C22—861no—
549C22—3441no—
550C22—3441no—
551C22—3441no—
552C22#121×D4311yescharacteristic
553C4—21no—
554C4—22no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—432no—
559C4—861no—
560C4—861no—
561C4—862no—
562C4—3441no—
563C4—1721no—
564C4C2×SD16×D4311yescharacteristic
565C4#135×D4311yescharacteristic
566C4#1458371211yescharacteristic
567C4#1458371511yescharacteristic
568C2—862no—
569C2—6881no—
570C2#1914412011yescharacteristic
571C2#465×D4311yescharacteristic
572C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radical#14583450C22
hypercenter#1672D43
hypocenterC43#19403
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
2. #477×D43C2semidirect
4. #19143674C2semidirect
5. #19134014C2semidirect
6. #19134013C2semidirect
7. #19134012C2semidirect
8. #19134011C2semidirect
9. #19133976C2semidirect
10. #19133975C2semidirect
11. #19133974C2semidirect
12. #19133364C2semidirect
13. #19133274C2semidirect
15. C43×#1672C2semidirect
293. #1672D43semidirect
353. C43#19403semidirect

Maximal subgroups

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

subgroupindex
#191457242
#477×D432
#191440682
#191436742
#191340142
#191340132
#191340122
#191340112
#191339762
#191339752
#191339742
#191333642
#191332742
#191332432
C43×#16722
#1940343