Finite Group Databasebeta

← #25082130

Subgroups — #25082130

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145731C211yesmaximal, characteristic, complemented
2#19144751C211yesmaximal, characteristic, complemented
3#19144656C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic, complemented
5#19134042C211yesmaximal, characteristic, complemented
6#19134035C211yesmaximal, characteristic, complemented
7#19134014C211yesmaximal, characteristic, complemented
8#19134007C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133993C211yesmaximal, characteristic, complemented
11#19133976C211yesmaximal, characteristic, complemented
12#19133969C211yesmaximal, characteristic, complemented
13#19133373C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C43×#1542C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583237—21no—
23#14583224—21no—
24#14583223—21no—
25#14583223—21no—
26#14583196—21no—
27#14583196—21no—
28#14583195C2211yescharacteristic
29#14583191C2211yescharacteristic
30#14583190C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583106C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583100C2211yescharacteristic
35#14583095C2211yescharacteristic
36#14583059—21no—
37#14583046—21no—
38#14583023C2211yescharacteristic
39#14583023C2211yescharacteristic
40#14583004—21no—
41#14582997—21no—
42C4×#10621873—21no—
43C4×D344—21no—
44#14582964C2211yescharacteristic
45#14582964C2211yescharacteristic
46C8×C22⋊D43—21no—
47C8×C22⋊D43—21no—
48#14582956C2211yescharacteristic
49#14582952C2211yescharacteristic
50#14582951—21no—
51C4⋊C8×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621884—21no—
72C2×D344—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063322C2311yescharacteristic
77#13063313—21no—
78#13063299—21no—
79#13063299—21no—
80C4×Dic86D411yescharacteristic
81C4×Dic86C2311yescharacteristic
82C4×D172—21no—
83C4×D172—21no—
84C4×D172D411yescharacteristic
85C4×D172C2311yescharacteristic
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063284D411yescharacteristic
89#13063282—21no—
90C42×D43—21no—
91#13063259—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063257—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063247—21no—
110#13063247—21no—
111#13063247—21no—
112#13063245—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063236—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#125×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150C2×C22⋊D43—41no—
151#10621898—22no—
152#10621898—22no—
153#10621898—82no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C42×C43—41no—
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182#10621885—42no—
183#10621884—42no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203D344—42no—
204#10621873—42no—
205C8×D43—81no—
206C8×D43—81no—
207C23×C43#12111yescharacteristic
208C22×D43—21no—
209C22×D43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—24no—
227C22⋊D43—82no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232D172—21no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—81no—
238D172#13512yes—
239C4×D43—24no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—81no—
243C4×D43—82no—
244Dic86—21no—
245Dic86—81no—
246Dic86#13512yes—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43C2×#12111yescharacteristic
262C2×D43—22no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43C2×#13511yescharacteristic
275C4×C43C2×#13511yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—22no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
284#3106—431no—
285#2988—431no—
286#1682—431no—
287#1681—431no—
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671—431no—
294#1572—431no—
295#1551—431no—
296#1542D4311yescharacteristic, complemented
297C2×C43—41no—
298C2×C43#304611yescharacteristic
299C2×C43#305011yescharacteristic
300C2×C43#306811yescharacteristic
301D43—42no—
302D43—161no—
303#533C2×D4311yescharacteristic
304#532—431no—
305C4×#41—431no—
306#500—431no—
307#498—431no—
308#486—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477—431no—
318#476—431no—
319#476—431no—
320#462—431no—
321#461—431no—
322#460—431no—
323#459—431no—
324#452—861no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336#432—431no—
337#431—431no—
338#431—861no—
339#431C2×D4311yescharacteristic
340C2×C4⋊C8—861no—
341C2×C4⋊C8C2×D4311yescharacteristic
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333C2×D4311yescharacteristic
349#333C2×D4311yescharacteristic
350#332C2×D4311yescharacteristic
351#332C2×D4311yescharacteristic
352#331—431no—
353#331—431no—
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—431no—
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—21no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#127—431no—
368#125—21no—
369#124—861no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—861no—
373#121—861no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—431no—
377C4×Q8—431no—
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4—861no—
384#117—21no—
385#117—431no—
386#117—861no—
387C2×C42—861no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—431no—
422C22⋊C8—431no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427C4×C8—21no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8—861no—
432#41—862no—
433#41—862no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—1721no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449C22×C4#1062189811yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452Q16—1722no—
453SD16—1722no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—3441no—
468C2×C8—3441no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C22⋊C4—41no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—41no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42#1062189811yescharacteristic
492C42D4×D4311yescharacteristic
493C42D4×D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—861no—
496C23—1721no—
497C23#1306329811yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—432no—
502Q8—861no—
503Q8—3441no—
504D4—432no—
505D4—864no—
506D4—861no—
507D4—3441no—
508D4—3442no—
509D4—1721no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—864no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—3442no—
525C2×C4—3441no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329811yescharacteristic
530C2×C4#1306329811yescharacteristic
531C2×C4#1306329811yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—862no—
549C22—3441no—
550C22—3441no—
551C22—3441no—
552C22—1721no—
553C22—1721no—
554C22C2×#1306329811yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—81no—
561C4—862no—
562C4—3441no—
563C4—1721no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4#135×D4311yescharacteristic
567C4#1458370511yescharacteristic
568C4#1458371211yescharacteristic
569C2—41no—
570C2—1722no—
571C2—6881no—
572C2#1914415011yescharacteristic
573C2#1914417511yescharacteristic
574C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1542C2
socleC22×C43C2×#121
prime radical#19144656C2
hypercenter#1542D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #19145731C2semidirect
2. #19144751C2semidirect
4. #19143704C2semidirect
5. #19134042C2semidirect
6. #19134035C2semidirect
7. #19134014C2semidirect
8. #19134007C2semidirect
9. #19133998C2semidirect
10. #19133993C2semidirect
11. #19133976C2semidirect
12. #19133969C2semidirect
13. #19133373C2semidirect
14. #19133288C2semidirect
15. C43×#1542C2semidirect
296. #1542D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457312
#191447512
#191446562
#191437042
#191340422
#191340352
#191340142
#191340072
#191339982
#191339932
#191339762
#191339692
#191333732
#191332882
C43×#15422
#1941943