Finite Group Databasebeta

← #25082104

Subgroups — #25082104

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#19145757C211yesmaximal, characteristic, complemented
2#19144760C211yesmaximal, characteristic
3#19144665C211yesmaximal, characteristic
4#19143705C211yesmaximal, characteristic
5#19134055C211yesmaximal, characteristic, complemented
6#19134049C211yesmaximal, characteristic, complemented
7#19134025C211yesmaximal, characteristic, complemented
8#19134019C211yesmaximal, characteristic, complemented
9#19133987C211yesmaximal, characteristic, complemented
10#19133983C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133372C211yesmaximal, characteristic, complemented
13#19133292C211yesmaximal, characteristic, complemented
14#19133249C211yesmaximal, characteristic, complemented
15C43×#1672C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×#10621902C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583243—21no—
23#14583243—21no—
24#14583242—21no—
25#14583239—21no—
26#14583209—21no—
27#14583209—21no—
28#14583186C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583109C2211yescharacteristic
32#14583105C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583064—21no—
35#14583060—21no—
36Q8×C43⋊C8C2211yescharacteristic
37#14583003—21no—
38#14582998—21no—
39Q16×Dic43—21no—
40#14582984—21no—
41C8×D172—21no—
42C8×D172C2211yescharacteristic
43#14582964—21no—
44#14582964C2211yescharacteristic
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950—21no—
48#14582950C2211yescharacteristic
49C4⋊C8×D43—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621873—21no—
70C2×#10621884—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063305—21no—
79#13063305—21no—
80#13063301—21no—
81#13063301—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84Q8×Dic43D411yescharacteristic
85#13063290—21no—
86#13063290—21no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89#13063287—21no—
90#13063287D411yescharacteristic
91#13063283—21no—
92#13063283—21no—
93#13063283—21no—
94#13063283D411yescharacteristic
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⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063249—21no—
113#13063249—21no—
114#13063248—21no—
115#13063248—21no—
116#13063248—21no—
117#13063247—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126C4×C43⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147#10621902—22no—
148#10621902—22no—
149C2×D172—21no—
150C2×D172C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159Q16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173#10621885—42no—
174#10621884—42no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
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—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43—41no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—41no—
193C4×Dic43—41no—
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202#10621873—42no—
203C8×D43—81no—
204C8×D43—81no—
205C8×D43—81no—
206C22×D43—21no—
207C22×D43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212Q8×C43#13512yes—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×Dic43—21no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43#12111yescharacteristic
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226D172—24no—
227D172—21no—
228D172#13512yes—
229C4×D43—24no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—81no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
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×C43C2×#12111yescharacteristic
254C2×D43—21no—
255C2×D43—22no—
256C2×D43—21no—
257C2×D43—21no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—22no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C2×#13511yescharacteristic
266C4×C43C2×#13511yescharacteristic
267C4×C43#57711yescharacteristic
268C4×C43#57811yescharacteristic
269Dic43—21no—
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#1673—431no—
285#1672D4311yescharacteristic, complemented
286#1671—431no—
287#1572—431no—
288#1552—431no—
289#1542—431no—
290C2×C43#304611yescharacteristic
291C2×C43#305011yescharacteristic
292C2×C43#306911yescharacteristic
293D43—41no—
294D43—42no—
295#533—431no—
296#533—431no—
297C4×#41—431no—
298#500—431no—
299#498C2×D4311yescharacteristic
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#477C2×D4311yescharacteristic
309#476—431no—
310#475—431no—
311#474—431no—
312#462—431no—
313#462C2×D4311yescharacteristic
314#461—431no—
315#461—431no—
316#452—861no—
317#452—861no—
318C8×Q8—431no—
319C8×Q8C2×D4311yescharacteristic
320#441—861no—
321#440—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324C8×D4—431no—
325C8×D4—431no—
326C8×D4—861no—
327C8×D4—861no—
328#432—431no—
329#431—431no—
330#431—431no—
331#431—861no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—861no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334C2×D4311yescharacteristic
338#333—431no—
339#333C2×D4311yescharacteristic
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332C2×D4311yescharacteristic
346C43#1941811yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—21no—
349C2×Q16—861no—
350C2×SD16—861no—
351C2×SD16—861no—
352C22×C8—861no—
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—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371C4×D4—431no—
372C4×D4—431no—
373C4×D4—861no—
374C4×D4—861no—
375#117—431no—
376#117—861no—
377#117—861no—
378#117—861no—
379C2×C42—431no—
380C2×C42—861no—
381#107—21no—
382#107—861no—
383#107—861no—
384#107—861no—
385#106—21no—
386#106—21no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
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—431no—
413C22⋊C8—431no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—861no—
419C4×C8—21no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424#41—862no—
425#41—862no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8D4×D4311yescharacteristic
431C2×D4—431no—
432C2×D4—861no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439Q16—42no—
440Q16—1722no—
441SD16—1722no—
442SD16—1722no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—3441no—
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—21no—
461C4⋊C4—431no—
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—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—21no—
478C42—431no—
479C42—431no—
480C42—431no—
481C42—861no—
482C42—861no—
483C42—1721no—
484C42—1721no—
485C42C23×D4311yescharacteristic
486C23—431no—
487C23—861no—
488Q8—21no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8—1721no—
496Q8#1306334612yes—
497D4—432no—
498D4—864no—
499D4—861no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—431no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—864no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—1721no—
515C2×C4—1721no—
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—861no—
533C22—861no—
534C22—862no—
535C22—861no—
536C22—1721no—
537C22—1721no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—22no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—861no—
545C4—861no—
546C4—861no—
547C4—3441no—
548C4—3441no—
549C4—1721no—
550C4#135×D4311yescharacteristic
551C4C2×#1306334611yescharacteristic
552C4#1458370811yescharacteristic
553C4#1458371211yescharacteristic
554C2—1721no—
555C2—1722no—
556C2#1914414211yescharacteristic
557C2#1914417111yescharacteristic
558C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC2×#10621902D4
hypercenter#1672D43
hypocenterC43#19418
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
1. #19145757C2semidirect
5. #19134055C2semidirect
6. #19134049C2semidirect
7. #19134025C2semidirect
8. #19134019C2semidirect
9. #19133987C2semidirect
10. #19133983C2semidirect
11. #19133967C2semidirect
12. #19133372C2semidirect
13. #19133292C2semidirect
14. #19133249C2semidirect
15. C43×#1672C2semidirect
285. #1672D43semidirect
346. C43#19418semidirect

Maximal subgroups

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

subgroupindex
#191457572
#191447602
#191446652
#191437052
#191340552
#191340492
#191340252
#191340192
#191339872
#191339832
#191339672
#191333722
#191332922
#191332492
C43×#16722
#1941843