Finite Group Databasebeta

← #25082106

Subgroups — #25082106

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145755C211yesmaximal, characteristic, complemented
2#19144754C211yesmaximal, characteristic
3#19144663C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic
5#19134054C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134028C211yesmaximal, characteristic, complemented
8#19134020C211yesmaximal, characteristic, complemented
9#19133986C211yesmaximal, characteristic, complemented
10#19133976C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133292C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1673C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583242—21no—
23#14583242—21no—
24#14583239—21no—
25#14583238—21no—
26#14583205—21no—
27#14583205—21no—
28#14583195C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583185C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583106C2211yescharacteristic
33#14583106C2211yescharacteristic
34#14583058—21no—
35#14583058—21no—
36C8×Dic86C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583003—21no—
39#14583000—21no—
40#14582991—21no—
41SD16×Dic43—21no—
42D4×C43⋊C8C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582949—21no—
49C2×Dic43⋊C8—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#500C2211yescharacteristic
61C43×#461C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70C22×C43⋊C8—21no—
71C2×C8×D43—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063316—21no—
75#13063316—21no—
76#13063305—21no—
77#13063305—21no—
78#13063301—21no—
79#13063301—21no—
80Q8×Dic43—21no—
81Q8×Dic43—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290—21no—
85#13063290D411yescharacteristic
86D4×Dic43D411yescharacteristic
87C4×C22⋊D43—21no—
88(C22⋊D43)⋊C4—21no—
89#13063283—21no—
90#13063283—21no—
91#13063283D411yescharacteristic
92#13063281—21no—
93C2×C4×Dic43—21no—
94C42×D43C2311yescharacteristic
95#13063259—21no—
96#13063258—21no—
97#13063257—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—21no—
116#13063248—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136#107×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621900—22no—
152#10621900—22no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159SD16×C43—42no—
160SD16×C43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—81no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175#10621885—42no—
176#10621885—42no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—41no—
179(C2×D43)⋊C4—41no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—41no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C8×D43—81no—
206C23×C43—21no—
207C22×D43#12111yescharacteristic
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—21no—
213D4×C43#13512yes—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—24no—
223C2×Dic43—24no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—81no—
229C2×Dic43#12111yescharacteristic
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—41no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—81no—
241Dic86#13512yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19418—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13511yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—21no—
269Dic43—22no—
270Dic43—21no—
271Dic43—21no—
272Dic43—41no—
273Dic43—81no—
274Dic43—81no—
275#3231—431no—
276#3116—431no—
277#3107—431no—
278#2988—431no—
279#1684—431no—
280#1683—431no—
281#1680—431no—
282#1679—431no—
283#1674—431no—
284#1673D4311yescharacteristic, complemented
285#1672—431no—
286#1671—431no—
287#1572—431no—
288#1552—431no—
289#1542—431no—
290C2×C43—42no—
291C2×C43#304611yescharacteristic
292C2×C43#305011yescharacteristic
293C2×C43#306911yescharacteristic
294D43—41no—
295#533—431no—
296#533—431no—
297C4×#41—431no—
298#500C2×D4311yescharacteristic
299#498—431no—
300#487—431no—
301#487—431no—
302#485—861no—
303#485—861no—
304#485—861no—
305#485—861no—
306#479—861no—
307#479—861no—
308#477—431no—
309#476—431no—
310#475—431no—
311#474—431no—
312#462—431no—
313#462—431no—
314#461C2×D4311yescharacteristic
315#461C2×D4311yescharacteristic
316#452—861no—
317#452—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320#441—861no—
321#440—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324C8×D4—431no—
325C8×D4—861no—
326C8×D4—861no—
327C8×D4C2×D4311yescharacteristic
328#432—431no—
329#431—431no—
330#431—431no—
331#431—861no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—861no—
334#335—431no—
335#335C2×D4311yescharacteristic
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332C2×D4311yescharacteristic
345#332C2×D4311yescharacteristic
346C43#1941811yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×SD16—21no—
351C2×SD16—21no—
352C22×C8—21no—
353C22×C8—861no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8C22×D4311yescharacteristic
358C4⋊Q8C22×D4311yescharacteristic
359#125—861no—
360#125—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×D4—431no—
372C4×D4—861no—
373C4×D4—861no—
374C4×D4C22×D4311yescharacteristic
375#117—431no—
376#117—861no—
377#117—861no—
378#117—861no—
379C2×C42—431no—
380C2×C42—861no—
381#107—21no—
382#107—21no—
383#107—861no—
384#107—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
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⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—431no—
414C22⋊C8—431no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—861no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424#41—862no—
425#41—862no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—861no—
432C2×D4D4×D4311yescharacteristic
433C22×C4—21no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—861no—
438C22×C4—861no—
439Q16—1722no—
440Q16—1722no—
441SD16—42no—
442SD16—42no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—3441no—
453C2×C8—3441no—
454C2×C8D4×D4311yescharacteristic
455C2×C8D4×D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4D4×D4311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—431no—
478C42—431no—
479C42—431no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—1721no—
484C42—1721no—
485C42C23×D4311yescharacteristic
486C23—21no—
487C23—431no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—432no—
493Q8—861no—
494Q8—3441no—
495Q8—1721no—
496Q8—1721no—
497D4—21no—
498D4—864no—
499D4#1306334412yes—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—3441no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—861no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—861no—
536C22—861no—
537C22—861no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—861no—
544C4—861no—
545C4—861no—
546C4—862no—
547C4—3441no—
548C4—3441no—
549C4—1721no—
550C4#135×D4311yescharacteristic
551C4C2×#1306334411yescharacteristic
552C4#1458370511yescharacteristic
553C4#1458371511yescharacteristic
554C2—42no—
555C2—1721no—
556C2#1914414011yescharacteristic
557C2#1914417411yescharacteristic
558C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1673C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1673D43
hypocenterC43#19418
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1673

Complements

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

NH ≅ G/Ntype
1. #19145755C2semidirect
5. #19134054C2semidirect
6. #19134046C2semidirect
7. #19134028C2semidirect
8. #19134020C2semidirect
9. #19133986C2semidirect
10. #19133976C2semidirect
11. #19133968C2semidirect
12. #19133374C2semidirect
13. #19133292C2semidirect
14. #19133251C2semidirect
15. C43×#1673C2semidirect
284. #1673D43semidirect
346. C43#19418semidirect

Maximal subgroups

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

subgroupindex
#191457552
#191447542
#191446632
#191437022
#191340542
#191340462
#191340282
#191340202
#191339862
#191339762
#191339682
#191333742
#191332922
#191332512
C43×#16732
#1941843