Finite Group Databasebeta

← #25081929

Subgroups — #25081929

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145735C211yesmaximal, characteristic
2#19144395C211yesmaximal, characteristic
3#462×D43C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic
5#19134024C211yesmaximal, characteristic, complemented
6#19134023C211yesmaximal, characteristic, complemented
7#19134022C211yesmaximal, characteristic, complemented
8#19133978C211yesmaximal, characteristic, complemented
9#19133977C211yesmaximal, characteristic, complemented
10#19133976C211yesmaximal, characteristic, complemented
11#19133975C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic
13#19133265C211yesmaximal, characteristic
14#19133251C211yesmaximal, characteristic
15C43×#1680C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583228—21no—
24#14583228—21no—
25#14583209—21no—
26#14583208—21no—
27#14583195C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583182—21no—
30#14583182—21no—
31#14583181C2211yescharacteristic
32#14583110C2211yescharacteristic
33#14583109C2211yescharacteristic
34#14583108—21no—
35#14583107—21no—
36#14583106C2211yescharacteristic
37Q8×C43⋊C8C2211yescharacteristic
38C8×Dic86—21no—
39C8×Dic86C2211yescharacteristic
40#14583023—21no—
41#14583023C2211yescharacteristic
42#14582951—21no—
43#14582951C2211yescharacteristic
44#14582950—21no—
45#14582950C2211yescharacteristic
46#14582938—21no—
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582906—21no—
50#103×D43—21no—
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72Q16×D43—44no—
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063323—21no—
80#13063316—21no—
81#13063305—21no—
82#13063301—21no—
83Q8×Dic43—21no—
84Q8×Dic43D411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290—21no—
89#13063290D411yescharacteristic
90#13063283—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#13063257—21no—
100#13063257—21no—
101#13063256—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#13063249—21no—
118#13063249—21no—
119#13063249—21no—
120#13063248—21no—
121#13063248—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#106×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
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
148Q8×D43—22no—
149Q8×D43—42no—
150Q8×D43—42no—
151Q8×D43SD1614yes—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—41no—
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43#4111yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86C2×D411yescharacteristic
163Q16×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177#10621885—42no—
178#10621885—42no—
179(C2×D43)⋊C4—41no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—42no—
206#10621872—42no—
207C8×D43—42no—
208C22×D43#12111yescharacteristic
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43C2×SD1612yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229C4×D43—24no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—41no—
233C4×D43—81no—
234C4×D43—82no—
235C4×D43C2×SD1612yes—
236C4×D43#13512yes—
237Dic86—21no—
238Dic86—24no—
239Dic86—41no—
240Dic86—41no—
241Dic86—82no—
242Dic86—81no—
243Dic86C2×SD1612yes—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19402—431nomaximal, Sylow
255C22×C43C2×#12111yescharacteristic
256C2×D43—21no—
257C2×D43—21no—
258C2×D43#46512yes—
259C4×C43—22no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C22×SD1611yescharacteristic
265C4×C43C2×#13511yescharacteristic
266C4×C43#57811yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—21no—
269Dic43—22no—
270Dic43—21no—
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274Dic43#46512yes—
275#3229—431no—
276#3078—431no—
277C2×#462—431no—
278#2982—431no—
279#1680—431no—
280#1680—431no—
281#1680—431no—
282#1680D4311yescharacteristic, complemented
283#1672—431no—
284#1672—431no—
285#1672—431no—
286#1672—431no—
287#1570—431no—
288#1546—431no—
289#1542—431no—
290C2×C43#304411yescharacteristic
291C2×C43C2×#46511yescharacteristic
292C2×C43#306911yescharacteristic
293D43—22no—
294C22×Q16—861no—
295#533—431no—
296C2×C4⋊Q8—431no—
297C2×C4×Q8—431no—
298#498—431no—
299#498—431no—
300#487—431no—
301#487C2×D4311yescharacteristic
302#483—861no—
303#483—861no—
304#479—861no—
305#479—861no—
306#477—431no—
307#477—431no—
308#475—431no—
309#475—861no—
310#475—861no—
311#475C2×D4311yescharacteristic
312#462—431no—
313#462—431no—
314#462—431no—
315#462—861no—
316#462—861no—
317#462C2×D4311yescharacteristic
318C8×Q8—431no—
319C8×Q8—431no—
320C8×Q8—431no—
321C8×Q8—861no—
322C8×Q8—861no—
323C8×Q8C2×D4311yescharacteristic
324#431—431no—
325#431—431no—
326#431—861no—
327#431—861no—
328#428—861no—
329#423—431no—
330C2×C4⋊C8—431no—
331#419—861no—
332C2×#103—861no—
333#334—431no—
334#334—431no—
335#334—431no—
336#334C2×D4311yescharacteristic
337#333—431no—
338#333—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332C2×D4311yescharacteristic
344#332C2×D4311yescharacteristic
345C43#1940211yescharacteristic, complemented, Sylow
346C22×Q8—431no—
347C22×Q8—861no—
348C2×Q16—21no—
349C2×Q16—861no—
350C2×Q16—861no—
351C2×Q16—861no—
352C2×Q16—1724no—
353C2×M16—861no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8—861no—
360C4⋊Q8C22×D4311yescharacteristic
361C4⋊Q8C22×D4311yescharacteristic
362#125—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8C22×D4311yescharacteristic
373#117—861no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C42—431no—
379C2×C42—861no—
380#107—861no—
381#107—861no—
382#106—21no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388C4⋊C8—21no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414C22⋊C8—431no—
415C22⋊C8—431no—
416C22⋊C8—861no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—434no—
427C2×Q8—431no—
428C2×Q8—861no—
429C2×Q8—862no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—1721no—
433C2×Q8—1722no—
434C2×Q8—1722no—
435C2×Q8D4×D4311yescharacteristic
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—1721no—
442Q16—42no—
443Q16—1722no—
444Q16—1722no—
445Q16—1722no—
446M16—1722no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1722no—
456C2×C8D4×D4311yescharacteristic
457C2×C8D4×D4311yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—431no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4D4×D4311yescharacteristic
477C22⋊C4—1721no—
478C42—21no—
479C42—431no—
480C42—431no—
481C42—431no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—1721no—
486C42C23×D4311yescharacteristic
487C23—431no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—432no—
494Q8—864no—
495Q8—861no—
496Q8—3441no—
497Q8—3442no—
498Q8—1721no—
499Q8—1721no—
500Q8SD16×D4312yes—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—431no—
509C2×C4—431no—
510C2×C4—864no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—3441no—
516C2×C4—3442no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C2×D4×D4311yescharacteristic
522C2×C4#41×D4311yescharacteristic
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—861no—
529C8—861no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C22—432no—
534C22—861no—
535C22—861no—
536C22#121×D4311yescharacteristic
537C4—21no—
538C4—22no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—432no—
543C4—861no—
544C4—861no—
545C4—862no—
546C4—3441no—
547C4—3441no—
548C4—1721no—
549C4C2×SD16×D4311yescharacteristic
550C4#135×D4311yescharacteristic
551C4#1458371311yescharacteristic
552C4#1458371511yescharacteristic
553C2—862no—
554C2#1914412311yescharacteristic
555C2#465×D4311yescharacteristic
556C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1680C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1680D43
hypocenterC43#19402
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1680

Complements

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

NH ≅ G/Ntype
5. #19134024C2semidirect
6. #19134023C2semidirect
7. #19134022C2semidirect
8. #19133978C2semidirect
9. #19133977C2semidirect
10. #19133976C2semidirect
11. #19133975C2semidirect
15. C43×#1680C2semidirect
282. #1680D43semidirect
345. C43#19402semidirect

Maximal subgroups

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

subgroupindex
#191457352
#191443952
#462×D432
#191436742
#191340242
#191340232
#191340222
#191339782
#191339772
#191339762
#191339752
#191333642
#191332652
#191332512
C43×#16802
#1940243